The maximum recommended towing weight is 3300 lbs (1500 kg), or 1600 kg (3500 lbs) in Europe. (Depends on whose lawyers are providing the advice, I guess.)

A class II hitch is rated for 3500 lbs.

Your biggest concern will be loading the trailer properly. The heaviest stuff must go over the axle at the floor level. Too much weight in the rear will leading to surging and sway. Too much in the front will take too much weight off the front tires of the car and lead to instability. Either one will create plenty of anxiety. Get it right, and you will hardly notice the trailer.

The lower the gear, the better the hill climbing. Don't worry, though. You've got plenty of torque available. You might find yourself using third gear to climb steeper highway hills. If you're climbing mountains, you might need second. On level ground, you should have enough horsepower available to use 5th if you want to, but 4th will work better with less strain on the engine.

Snow is definitely a complicating factor, particularly if the nose of the car is unweighted. Do you have snow tires?