Ponying a young horse some is OK, but I have found that 2 problems 'can' arise out doing a lot of ponying without taking preventive measures.
If you do not pony a horse from both your right and left side, they will be 'limber-necked' to the left and stiff to the right when you start riding them.
Some horses get really 'hung up' on a pony horse and want to go to another horse when you start riding them. They can have a really deep-seated problem with being 'buddy sour'.
When I have ponied horses a lot, I always made sure they carried their heads as straight in front of them as I could get them to and ponied them more on the side that wanted to be stiff.
When I was done ponying any horse, I stopped somewhere beside the barn with and tied it up. Then, when the horse was good and quiet, I hosed it off if it was sweaty and again tied it out a long way from other horses. This helps prevent a horse from wanting to go back to the barn with their buddy.