Depends what you mean "cold weather hunting"....of course if you are in a survival situation that's one thing. If you are tent camping to hunt in weather down to say 10-20F or so propane would be my choice. I've used it lots in my Cabela's 4 man Alaskan tent with no problem from moisture (little buddy type heater), maybe efficient venting is the problem some folks have?? I like wood stoves and wall tents when there is time, but on a DIY hunt by myself, when I can bring what I want (not packing in) there is no way I'm going to have the time to fool around with wood heat, just not enough hours in the day.
As far as the fumes from vent free heaters go, that is what these are made to do, if there was a real CO problem I don't think they would still be on the market.
R