Here's a few items to consider:
1. Slow down, you don't make miles if you're sitting in the ditch.
2. Slow down before the corners, especially the sharper ones. I've seen way too many people towing with light short wheel base 1/2T trucks that when they get to a sharp corner, they let off of the gas and use the brakes very quickly. What usually happens is the trailer weight is greater than the truck so it keeps pushing straight ahead usually jack knifing the the truck and TT pushing both into the ditch. Yes, you're towing with a LB 3/4T so you're much better off, but don't try to slow down suddenly in the sharper corners.
3. On the TT brake controller, you might want to lessen the brake setting a little bit. Where you have it set for dry pavement may allow the the TT tires to lock up and slide on slippery snow.
4. If you don't have lots of weight in the back of your truck, put some in it.
5. Traveling at night might be a better option. Note that I said "might be" because a lot of the traffic should be off of the road. You're not only watching out for yourself, but all of the crazies in their new SUVs with crappy all-season tires that are going way too fast and can't stop until they hit something.
6. Speaking of bad all-season tires, if you're going to be in the snow, you might consider putting a good set of real snow tires on the rear of your truck if you don't have them. You can always take your other tires with you can have them changed when you get down south.
Bill