I wouldn't. And I'm 6'2" and know how to "take care of myself." At a minimum I think you'll return without your watch, flashlight, thermos, and sleeping gear. Not all of the homeless are baddies, not by a very long shot, but there are those who prey on them, take what little they have, beat them, set them on fire.... And I happen to know that you ain't no spring chicken.
Ebbie, folks are trying to get into the shelters for a reason: learn from that. You don't need to stick your hand into the fire to understand you can be burned.