I know that there are well vented cabin heaters that are as safe as propane stoves and ovens. I have had propane ovens and stoves and continue to be personally comfortable with that. As Paul noted, his cabin heater is a quality unit that is just Personally, with CO detectors (and maybe a propane leak detector). I think a propane cabin heater like Todd has is fine.
I'm not a fan of on demand gas hot water heaters.