A little off topic, but cold weather camping is the same whether on a bike or skis. The new blends of fuel for canister stoves burn well in sub-freezing weather. Our shovels make good windbreaks. For tours longer than a weekend we use a MSR Whiperlite, liquid fuel stove which is more efficient. What is the advantage of a wood burnibg stove if you have to carry a sleeping bag that will handle the lowest nightime temperatures anyway?
I usually just put the stove on the pot lid so it does not sink into the snow or fall over. That tent, sleeping bag, thermarest pad, stove, fuel, and utinsels, weighs about 15 lbs. Light enough to use on a winter bike trip. I use the exact same set up, only with a lighter sleeping bag, during the summer, whch gets the weight down to just over 10 lbs. This setup was very comfortable in some pretty cold weather for a 3-season tent.
Even this setup is good in a pinch. An insulated parka and pants (carried anyway), a foam pad, sil-nylon tarp, and a bivy sack are comfortable; and weighs about 5 lbs. If it gets too cold, a fire can be built near the opening.