That depends on the racetrack, racing commission rules and regs. A few Breeders’ Cups ago one of the European favorites for one of the races while going to the post with the required lead pony and was injured and scratched. The horse like probably all euro trained horses wasn’t used to a lead pony in tight quarters.
He got annoyed/bothered by the pony and kicked, cow kicked at him. Missed the pony but hit the post of the guard rail or I think it was the parked horse ambulance. A google search would give the details. I seem to remember the commentators saying that the euro horses are’t used to lead ponies but are required to use them. Again, a fact check maybe called for on my comment.
Personally I think it should be left up to the trainer. Especially with International Stakes and horses, Breeders’ Cup races.