I'm a big fan of the Dick Cepek Mud Country tires....Tire rack has them priced reasonably. Same carcass structure as the other decent offroad tires - 5 ply tread / 3 ply sidewalls. Made by Cooper Tire. They're actually round and balance well, and they're not terribly noisy compared to other mud tires, and they're much cheaper than MTR's, etc, which can be tough to source in 35x12.50/15. I have 35s. Difference in truck height between 33s and 35s is only an inch for garage clearance. The meany just barely fits in my garage with the roof rack.
As for running AT's, yes, you'll probably be fine unless we get wet weather, which is impossible to predict. We will see some higher elevations that could have some snow as well, but then again, it could all be dry and nice. What I can say is none of the trails are overly technical when dry. Add mud and snow and that could be a different story, but like I said...impossible to predict.