Small buddy heater or other made for heating propane
heater should work better than the stove. On the other hand if you make coffee or tea in the morning....
... I can say that in a 13 ft. scamp
the chill will be "off" before the coffee is done perking on the stove. Essentially any cooking will take the chill off. Hot water for tea or instant oatmeal. Toasting a bagel on a folding stove top rack etc. It will be warm before the cooking is done.
Aside from CO concerns one will also be pumping a lot of moisture into the air with an open propane
burner. Damp may make things less pleasant than the cold.
On shore power the small cube heaters can easily heat a small camper. In Wyoming with snow on the windshield of the car in the morning we were fine all night usina a small cube heater.
Hot rocks from campfire wrapped in towel can stay warm all night and make a very nice foot warmer.