In order to figure out how to keep heat in, we have to understand how we lose it through our footwear. I'll try to go light on the thermodynamics but a basic understanding is essential.
Conduction is the loss of heat through your insulation. If the air temperature is 0 degrees and your feet are about 96 degrees F, the difference between the two creates a gradient - like water going down a stream from a higher point to a lower point. You can imagine a thicker sleeping bag as a slower stream since the difference in temperature is spread across more insulation. A lower outside temperature also makes a steeper, faster stream and we lose heat even faster.
Most insulation we use for hiking boots like primaloft or thinsulate relies on small fibers to trap pockets of air and prevent heat from escaping since air is a natural insulator. Dry air and dry fibers resist losing heat through conduction extremely well, like the insulation in your house. Water, such as the water in your sweat, transmits heat efficiently - about 25 times more than air. When the two mix, we lose a lot of insulation value and transfer much more heat through our footwear.
Convection is loss of heat due to the movement of air or another fluid like water, so if our footwear is too loose causing air is being pumped due to the movement of our feet we will feel cold. Convection is how we can describe feeling a draft, a cold burst of air pulls heat away from our body and runs.
Radiation is heat transfered by warm bodies emmitting photons, it happens with all matter above absolute zero. We gain heat from the sun through radiation but also from anything hotter than us, like stale chicken fingers under a heat lamp. Our feet actually lose some heat to radiation, though it's not as significant as conduction and convection. The bigger the difference in temperature between two surfaces (with an air gap) the more heat loss from radiation. Some companies add a reflective liner to clothing but in order for that to work you need an air gap between us and the reflective layer and a very high temperature gradient between the reflective layer and whatever is next to it. I haven't noticed any significant difference with this technology, though you can see how it would work in a space blanket.
Phase Transitions cause heat loss or gain, depending on the phases. For instance, it takes 4.2 kilojoules (a measure of energy) to raise one liter of water one degree Celsius but 2270 kilojoules to transform that liter of water to vapor. A more relevant comparison would be 155 kilojoules to raise 1 liter of water from ice cold to body temperature, then almost 15 times more energy to evaporate it!
This is why we get so cold in wet clothing, part of our body heat is causing the water to evaporate which takes an enormous amount of energy. Melting snow or ice with our bodies, such as eating it, also uses an enormous amount of energy.
From this very basic understanding of heat transfer we can glean a lot of information about how to keep our feet warm. We know that dry insulation prevents conduction many times better than wet insulation. We know it takes nearly 15 times as much energy to evaporate water than it does to raise it to body temperature and we know we can lose a great deal of energy from the movement of air. We also can see that reflective linings only work in very specific situations and not in the cramped confines of a boot. For more information see: http://en.wikipedia.org/wiki/Heat_transfer
We also need a basic understanding of how our bodies regulate temperature.
If part of us is too hot, our skin will sweat. This is because our bodies have evolved to take advantage of the loss in energy from sweat evaporating into the atmosphere. Conversely, our feet and hands rely on warm blood flowing from our core to regulate their temperature. If our feet get too cold, the blood vessels constrict, reducing blood flow. This is to keep our core warm at the risk of losing our extremities to frostbite.
The combination of heat transfer and our bodies reaction to cold and warm creates the most common cold-feet scenario - over insulation, followed by sweat, followed by cold feet that just won't warm up. Our feet start out too warm or get too warm from periods of high activity like hiking uphill, so they sweat to cool down. The sweat slowly wets the insulation faster than it can either wick somewhere else or evaporate through the "waterproof-breathable" boot shell. Even if our boots were very breathable, we would now be losing even more heat due to the phase transition of water! Breathable or not, the liquid water reaches the inside of the boot shell and acts as a conductor for heat to leave our feet and enter the atmosphere since the insulation is no longer dry and full of air. Now our feet can't stay warm enough, so our blood vessels constrict and we feel even colder! Ironically, the most common reaction to this situation more insulation, which just adds more space to water to collect before the boot gets cold. This actually works for many people if you pull your sweaty feet out of your boots at the end of the hike and never had cold toes.
This is because are inclined to over prepare for things we fear most, so many of us will take extra insulation thinking it's needed to stay warm. You see this all the time with new winter hikers that start out in too many layers, sweat our their insulation and get cold not realizing they should wear less while hiking hard and more when stationary or going downhill. It's a big turn off to winter hiking if you start thinking there's no way to stay warm even with all that insulation! It's also very easy to sweat without realizing, especially in your footwear. For our core we can take layers on and off very easily but no one changes their boots out when their feet are sweaty!
So how should we keep our feet warm? To me, there are four things that will cause cold feet (assuming the our core is warm), and each can be prevented.
If the blood flowing to your feet is cold, they will be even colder. Add a shell over your hiking pants or knee high gaiters over your calves to keep the blood going to your feet warm. If you notice your legs are cold when your feet are cold, this is your most likely problem. My gaiters enable me to wear "waterproof" un-insulated trail shoes into the 20's and still keep my feet warm. Knee high socks will also help since you likely don't need as much insulation on your thighs which are thicker and closer to your core.
Restricted Blood Flow
If your boots are too tight because you stuffed warmer socks in them your feet won't get enough blood to stay warm. If you pull your cold feet out of your dry boots and socks but your legs are warm, this is the most likely problem. Size your winter boots on the loose side to allow for thicker socks. I prefer a lighter insulation on my boots and thicker socks since you can change out wet socks mid-hike but not wet boots. You can also wear thinner socks for warmer temperatures and tighten the laces to take up the extra space without needing another pair of boots. However, if the boots are too loose we'll lose heat through convection - air moving in and out of the boot.
Another tip for cold toes is to swing your feet or kick the air to force blood through them faster. This also works for your hands - swing your arms to a sudden stop to move warm blood through them. If you're sitting at camp or on an extended break, sit with your feet closer to your heart's height so there's less resistance for the blood to work against.
Dehydration also restricts blood flow by thickening the blood and can be common in winter when hikers don't want to stop to drink. Monitor your pee color and frequency, though I find snow makes pee look more yellow than normal.
This is what I've spent the most time talking about, so hopefully you've got it by now. The insulation gets wet, transfers heat and evaporates water leading to cold feet. The problem is we go from hiking hard up hill to standing around at the summit or at camp to hiking easy downhill all in the same boots. You can change into dry socks if the conditions allow and if you have any. Alternatively, vapor barrier liners (VBL's) work to prevent sweat from entering the insulation. In very cold temperatures or if I intend on camping, like at my 48 finish, I wear a ham roasting bag from the grocery store over a thin liner sock under my wool sock. The combination fits snugly in my boots and keeps my insulation from getting wet. My feet still sweat and get wet but at least they're warm!
Lack of Insulation
I saved this for last since I really think it's the most unlikely situation in NH winters if you're already wearing warm socks and any kind of insulated boots. However, if you have Raynaud's - a lack of blood flow to hands and feet - this is probably your problem. If your legs are warm, your feet are not restricted in your boots and your socks are not sweaty at the end of the hike - you need more insulation. Look for boots with 400 grams of thinsulation vs. the usual 200 or with (meaningless) temperature ratings of -40 or lower. You can also size your boots up for fitting chemical toe warmers in there, which generally last most of the duration of a day hike.
So you know understand how we lose heat and the most common causes of cold feet. Hopefully I've solved some footwear problems for you, at some point I'll do a more specific post on types of winter footwear but those are the basic principals. Let me know if you have any questions in the comments!