I wouldn't but I also live on acreage and have a well-ventilated shed that's a good distance from other buildings. If you have any place, even leaving them outside it would be safer. I have 4 of the 20Ibs canisters and usually leave one next to my grill year round, the grill is covered but not the canister and weather hasn't affected it. I don't exchange my tanks as my local farm store re-fills them at less cost than exchanging them so at least one of mine has spent a good deal of time outside with no damage outside of a little rust.

I have a camping grill that takes the one pound canisters and after leaving them in the shed for a five or six years or maybe more, some seemed to be empty so they may have leaked, which would make me a little nervous about them in an enclosed garage.