In my opinion Jim, 'barrel racing' wouldn't fit well. I doubt you'd be able to make it readable. Possibly if you added the barrel behind the horse, attached to the tail/rump it could be done. But you'd have to make it a fairly large puzzle. When i was a kid doing contest, we just called it 'Barrels' Nobody really said barrel racing, I think you'd be okay to have the puzzle just say Barrels and it would still make sense. Just my opinion of course.
Russell
Oh, I'd add a cowboy hat to the chick in these photos as well, if it were me.