They push down on the wheel, but will generate twisting loads on the frame as the trailer tries to tip from side to side.
Obviously if you are rolling along on a smooth road and not cornering sharply these loads will be pretty small. if you're out of the saddle honking up climbs you'll notice it pretty sharply as the whole bike starts wobbling about beneath you!
You learn to use your upper body to steady it, but also to pedal more smoothly
That was well put I tried my trailer on my old S/works rigid hardtail and the wheel was not as tightly built as I should of done, 15 hilly miles later and the back wheel lost all its tension and er wobbled alot
Moral have a good tightly tensioned wheel