Fire in deeps snow - survival

I've made them before but that requires a chainsaw and cutting down and entire tree. This was the other day when I was practicing my fire building.the snow was hard and we could walk around but no chain saw. Way to heavy to pack in on the bike.

This is one we built this summer! Burned for a long long time!

Generally, in very deep snow, rather than build a problematic fire.
It usually better to use any one of the lightweight portable backpacker type stoves.
(alcohol, flammable gas, or liquid fueled)

Obviously, building a fire ON snow or ice, will result in the snow/ice underneath it melting.
As already suggested, an aluminum, steel or stainless steel cookie sheet is helpful.
But, you need to "crib" up some thick cut branches or small sawn logs to set the cookie sheet on.
So that there is cold "air" space circulating under the cookie sheet.
Which will slow the snow/ice from melting under the cribbing.

LOL, when I was a little kid in Alaska, out camping in winter.
We would cut down a 7 or 8 inch thick green tree.
Saw little logs for a flat on the snow fire platform.
Platform would eventually heat up & begin sinking into the snow.
Experience taught us to crib up the platform up off the snow, to slow that down.

Any sort of platform that will help spread out the heat and weight is helpful. When the snow is packed down, it's pretty solid, and the snow itself is a good insulator so spreading out the fire helps spread out too much heat going to any one area. Like Bunker mentioned, adding more insulation by putting split logs or raising it up will help block the heat to the snow, as long as it doesn't burn through whatever you've put down.

The aluminum foil is a good idea, you might just need to bring more of it next time. The other thing you can do is put some insulator between your fire and the foil. Either quick burn a bunch of leaves or start a smaller fire before going on to the main one. Then take the ash from the first fire, and use that to coat your next set of foil. Ash is a good insulator as well and can protect the foil from a bit of the heat.

Also keeping your fire smaller and not quite as hot means that it's not going to put out as much heat into the snow and melt it down or burn through your foil. I think a lot of people don't know that you don't need a big fire to get a decent amount of heat for yourself, especially if you're enclosed or using a decent reflector. If you're using pine or other light woods, they tend to burn a lot quicker and hotter than something like oak, so planning your fuel can be helpful.

On the other hand, like a couple of other folks have said, if you're using fuels just bring a small Coleman and a good sleeping bag and save yourself the hassle!

I will carry a stove when winter camping but as a Survival system it's a little much. This is what I carry for normal riding. Every thing I carry survival wise has to stay on my person. If I lose my bike in a slide or in a creek I need to be able to make it on what I have on my back. I'm going to try some of these ideas soon.

I do also make a snow cave when I can. And yes that is my primary mission should I get stranded over night. Still they are not fast to dig right and if the snow is fluffy it's even harder.