No U Haul trailers do not have trailer brakes to hookup to the tow vehicle.
Although really the larger car trailers from U Haul should indeed have trailer brakes but when I rented a U Haul car trailer it did not have any trailer brakes on them.
So unless they change their trailers then no U Haul trailers do not have trailer brakes which is really needed when you're hauling something heavy and are going down hills.
I towed a heavy vehicle on a U Haul Trailer without trailer brakes and there was no problem but it can be a safety issue and U Haul should really have trailers with brakes.
But I doubt they will ever have any trailer brakes on their trailers.