No, it is Luck of the Draw as to the horse a competitor gets for training. I have friends who do these all the time. Sometimes they luck out and get horses that are super to work with, other times, the get the typical "wild mustang".
It depends on the Challenge I believe. There are some auctions where the horses are ear marked for the competitions and if a trainer wants that horse they have to purchase it by high bid.
Wylene Wilson (featured in the film) just won the Mustang Magic last weekend. I know she has kept one of her Mustangs from the past. I'm not exactly sure how it works, but in some of the competitions you actually select and purchase your own horse. In others, you are given the horse by random draw, then the auction proceeds are used to fund additional programs.
I had a friend participate in the mustang makeover. They did not get to choose which mustang they were given. After the competition they could keep their mustangs or sell them in the auction held after the show. She chose to keep hers.
Mustang makeover
