Well, we live in Montana. and on occasion we can start out in June or August on a balmy day and have snow the next. Months on either side of those can bring plenty of snow sometimes.
The biggest thing about towing in snow is to slow down. Increase the distance from vehicles in front of you by 3 times the normal 2 second interval. Don't back up traffic behind you, pull over and let them pass, then resume your trip. Don't get in a hurry. The second big thing is to be prepared, full fuel, full propane
, drinking water, food, coats, tire chains, shovel, etc....
I have pulled my Scamp
through several blizzards, until I found better weather or until there was place to safely pull off and wait it out. Stay out of chain-up areas alongside the highway, Trucks skidding in and out my not see you in the storm and hit you. Find rest areas or campgrounds, parking lots, etc.
I have pulled in steep snow and ice covered roads to go hunting in November with 4 wheel studded chains on and the rear differential locked for all the traction I could get.
Snow is nothing to take lightly, but by being prepared, with chains, and a complete winter gear setup in the tug and trailer, it will only add a bit of time to the trip and will allow you to sit it out better when you stop.
Just use common sense and enjoy the trip.