Whether the wind is steady or gusting, as long as it's strong, it will have an effect on any trailer out there. Tractor trailers, campers, boats -- as long as it's being pulled along the road, the wind can push it around.
Think about it: The trailer has no power of its own to turn its wheels or slow down. It is attached to the truck towing it at one little point: the hitch. It usually has big, tall, square sides that are the exact opposite of aerodynamic. The wind isn't going to come at the trailer in a polite, aerodynamic way either; it's going to shove against it from the side, like a bully.
This is the point where, if you want to do it wrong, you're going to try to draft behind that trailer in front of you on the road. Get really close, so that the nose of your vehicle is nearly tucked under the bumper of the trailer. This is a poor practice on the best of calm, sunny days, but on a very windy day, it's downright dunderheaded.
For extra dunderhead points, pull out real quick-like from that drafting position and try to pass the whole rig as it sways in the breeze. See where that gets you. (Hint: It does not get you positioned perfectly and safely in the center of the lane.)