Unless you're using a set-up specifically designed for it (like a canvas-walled outfitter's tent and folding wood stove), this seems like a great way to die.
I've never bothered with it, even winter camping. That's what the down bag is for.
Sorry for not making that clear: Heating the tent is NOT for sleeping, it is for making life enjoyable and dry. One of the great comforts of life is drying your clothes after a long day... starting the next day with dry clothes.
When sleeping, I agree the winter sleeping bag takes care of the comfort.
I suppose the "great way to die"-comment is related to carbon monoxide. It poses a very real threat, but that treat is eliminated COMPLETELY by making sure there is ventilation - and it is not a good idea to "leave the heat on" when you go to sleep. That rule applies to ALL burners and stoves (wood, white gas, parafin). Doesn't matter what fabric the tent is made of, ventilation is ventilation.
Lots of other good advice in this thread. (Get adequate sleeping pad + sleeping bag, a nice, warm meal before bed time and so on).
I really don't understand what appears to be standard tent in America: A separate rainfly which goes over the proper tent (which is not waterproof). Must be a bastard to put up that rainfly in high winds... and doesn't really lend itself to being the most windproof design once erected. But hey, that's probably just because I've never tried it.