no, If you want to cover it, get an RV cover that fits your TT. Having a trap flap around in the wind could damage the sides.
I leave ours next to our house and never covered it and never ran into any issues with the snow, rain, etc. on the roof. Think about it, dealers don't cover them on their lots, the manufacture doesn't cover them either while they sit there to be transported.
2013 Prime Time Tracer 3200BHT
2016 GMC Crew Cab Duramax All Terrain
Ribs in the smoker and Whiskey in hand