Weather is irrelevant; the question is can propane be used safely indoors and the answer is yes. There are millions of rural house holds in the USA to prove it. Next question can it be used safely in a basement? The answer is yes and the numerous basement apartments I have seen and lived in prove that.
Propane can be used safely indoors even in a basement if common sense is applied and appropriate research is conducted. I have used propane most of my life in basements, houses, garages, heck even in tents, in sheds and even in the deer blind.
Should a person use a turkey fryer indoors? NO
Should a person use an outdoor rated burner indoors? NO
The general statement "OMG don't use propane inside you'll die or burn down your house" is basically not reality. Many Americans who choose to live in rural environments use propane because it is an economical and efficient energy source and is safe if used appropriately. Should everyone stop using electricity because some idiot electrocuted himself trying to wire his brewery, or natural gas needs to be outlawed because a brewer burnt up his shed. Please lets get real.
Ok Rant Over...