A really good WDH is a must, I have the Equalizer round bar, and I got to say, pulling through the Virginia and West Virginia mountains, severe storms in Illinois, was very windy at times, And not driving foolishly, You shouldn't have any problems. I used to tow our 26ft hybrid with a F150 V6, same WDH. You got plenty of truck for a shorter TT.
We currently have 33ft TT huge profile, that we pull With The Toyota Tundra, We are always mindful of mother nature, no shame in pulling over side of road or Truck stop to wait bad weather out.