All foals are born with the Untrained trait. I don't think you can get rid of it until their old enough to ride. Anyway, Leading my foals didn't seem to have any effect on the Untrained trait, but leading adults for the first time since Ageing Up showed it going down a little. However, standing around with the horse on a lead all day seemed boring.
But I always just Mount them, and Gallop over to the Equestrian Center, and "practice jumping" on the Calavetti Trainer course - it trains them, while building Jumping and Racing skills for the horse, and Riding skill for the rider all at once! Very effective.