As a boy scoutmaster I asked the troop to go out and in the woods in waist deep powder to start a fire. The scouts were more than up for the challenge. Boy just love to start fires. They were armed with 100s of matches and at least 6 bic lighters. Over 2 hours later no fire. They were getting pretty frustrated. I finally gave them the one piece of information they needed. You can't start a fire on top of 4 feet snow. I told them they had to dig down to ground level and start the fire there. Five minutes later they had there fire.
Actually you can light a fire on top of the snow if you have to but you must prepare a base first. Create a bed from boughs or pieces of firewood on top of compacted snow. It works, after a fashion. The fire will melt a hole for itself and drop into the snow, perhaps eventually extinguising itself. We used to build fires on top of the ice on the frozen lake as well while we were ice fishing. The bottom most portion does not burn completely and you will end up with a few pieces of charred wood in a pool of water. Obviously digging down to ground level if you can is good advice and more likely to produce a good outcome.