RS I'm kind of an old-cabin nut and whenever I see sheet steel on a (genuine) old cabin it's even thinner than than 22ga, and nailed down with lots of small nails. Usually from a 55gal barrel or oilcan, and usually LESS than 22ga.
People used what was "available" in the old days, and the old days is what I'm trying to do. Nowdays people buy the material that won't get the contractor called back for remediation (usually on advice from the contractor). Not an issue here.
I'm going to use (uncoated, rustable) nails every 1.5" so it has that old look. I've built lots of stuff, I know about steel, know that 22ga is plenty thick for this.