Living in Montana, towing our Scamperoonie in snow can happen for about nine to ten months of the year. The picture attached was this past June.
In snow conditions, slow down, and if the conditions turn to white out, find a spot to pull over and wait it out. The biggest blizzards are over usually in a few hours to a day at max. Point the tug into the wind if you can when you park. It is better to wait it out and be alive and unbanged up than in a pile up in a white out.
If lot of people are passing you, pull over and let them pass, maintain double or triple the distance to vehicles in front of you for adequate stopping distance.
And yes good tire chains for your tow vehicle are strongly recommended, mine stay in the rig year round, studded chains for the rear
axle and a diagonal cable set for the front when it is really lousy. That being said, my personal rule of thumb is if four wheel drive is needed on paved roads or highways, when pulling the trailer, then before I will usually put on my chains, I'll pull over and wait it out when the going is sufficiently bad enough to warrant using chains. I can deal with being a bit late easier than being in an accident.
Just be careful out there.
Garo