You should be fine, but having some type of firm footing (2 x 6 pressure treated planks, etc.) under the tires and jack stand will minimize any impact from ground frost heaving, tires freezing in the ground, spring settling, etc. Park the HTT where surface water doesn't collect after a rain shower or snow melt as well.
Also have the tongue raised a little so that the roof water runs off the back of the HTT rather then over the front angled surface, and leave the corner stabilizers in the raised position.
Putting a couple small containers of Damp Rid (Walmart, etc.) in the HTT wouldn't hurt, along with a couple of mouse traps......, I do during my TT's winter storage.
2016 GM 2500HD 6.0L/4.10
2005 Jayco Eagle 278FBS
Reese HP Dual Cam
Putnam Class V