Make sure your tow vehicle tires are snow rated with the little snowflake, and don't make any sudden moves. From the time I was 16, I towed trailers behind my car summer and winter with 4 bandmates packed in the vehicle and in sometimes harsh winter conditions on the Canadian praries and in the B.C. mountains. I would advise giving yourself lots of stopping distance and no quick steering or braking corrections. I know it's just common sense. I personally don't think towing is a big deal in the winter, just relax with it.
While I'm comfortable driving my tow car in snow ( live in an area that gets 150"-200" of snow during a bad winter), my one experience towing the Escape on ice has convinced me that I will wait out ice & snow. Trailer brakes are pretty squirrely on snow!
If you have summer tires - which would include every ST (Special Trailer) tire available - on the trailer, then the trailer certainly will be squirrely under braking. This is like a front-wheel drive car: if you put winter tires on only the front, the rear will slide around and your life can become unintentionally exciting.