We've been thinking about it, too. I was a terrible mountain biker, but I think I could handle snow better than rocks and roots. And, I might not be adverse to riding one on the crappy roads, after a storm.
There don't seem to be many options for short people, though. I found a junior fat bike that did meet my measurement requirements. The smallest woman's fat bike I've seen is 15 inches, which is the size of my mountain bike, which was too big.