This website has a lot of info on hot tent camping (using a wood stove in a tent).
Sadly, their website was hacked and they lost a lot of info on their forums, but there's still loads of good information and experienced people on their forums.
There is also the book by the conovers and its earlier editions. It's fun to read, but definitely not light. These methods are inspired by the native peoples in the forested regions of the north (i.e., Quebec, Maine, etc.).
Snow Walker's Companion: Winter Camping Skills for the North by Garrett Conover and Alexandra Conover (Oct 26, 2005) ISBN-10: 0976031337
It's out of print and Amazon's used prices are outrageous. Look it up in bookfinder.com and there are some reasonable prices.
The standard for hot tent camping is cotton tents. Nylon is vulnerable to damage from sparks and heat. You'd have to modify the tent to put in an inflammable piece for the stove pipe. I don't think I'd try it with a nylon tent, but the kifaru tipis are nylon so I guess it can work.