The footings purpose is to spread the load over a greater area reducing the likelihood of creating a point load that will slowly go deeper. With enough sonotubes and/or large enough sonotubes the load may be well enough distributed, or not. It depends on what the soil is like, how many psi load it can withstand.
As for depth it depends on expected maximum frost depth. That really varies in the mountains. The best is to ask the county or state engineer or building permit office. I did and got a puzzled look.
They guessed that 30 - 36 inches should work. Guessed.
I had already guessed that would be a good depth for our 8800 foot location. We did about 40 inches. Since you're lower and a little further south 36" would be fine, and probably even a little less would be workable. That's a guess.
My son and I hand dug our holes using a Ridgid post hole digger. It is better than other hand tools because it has articulated handles to reduce the handle spread needed. That can be a bother when going deep. They also cost more than others. We dug a 12 inch, more or less, hole and belled the bottom out with a bent pipe tool, then poured a 16+ inch footer.
8" tubes would be suitable