The GVWR of the F150 is going to be the problem with a 32' trailer. The tongue will/should be heavy, and that is gonna cut into what else you can carry in the truck. Depending on the tongue weight, a couple of passengers and some camping gear in the back might send you over the weight limit.
With my 2006 F150, with a 700 lb. tongue weight, me, the missus, the dog, and some gear in the back, I am withing 100 lbs. of my GVWR. I am OK now with a 28.5 footer, but if I get anything bigger, I am gonna have to get a 3/4 ton truck.......and would think about a 1 ton since there isn't that much price difference.
Chap , DW Joy, and Fur Baby Sango
2006 Ford F150 Super Cab 4x4
2008 Surveyor 263