I tow a 26 foot TT with my Silverado 1500 5.3 4x4 all over Montana, and it handles the mountains and winds fine. However, I bought the truck long before I ever considered buying a travel trailer and if I could have done it over again, I would have gone for at least the 2500 with the 6.0 or perhaps a diesel. We are now thinking of moving to a fifth wheel and there is no doubt we have to start with a bigger truck. This time we will go for a 3500 diesel SRW.
Good luck with the 2500. I think the 6.0 2500 will be a great vehicle for your needs.