People do it all the time! We have 7 tanks, 30 gallons of gas and 10 of diesel here at the ranch so we scrounged an flam cabinet and put all of that inside the cabinet OUTSIDE of the barn. Two open flame heaters in the barn so we figured safety probably should take presence over convenience.
Only problem you could run into is storing a 20# cylinder indoors during the summer that was filled in the winter, it's possible for the tank to vent due to being over filled. This scenario is the reason 20# cyl. are equipped with over fill protection, but they are not foolproof.