Riding schools & tack?

I don't know if this was asked already or if I missed it somehow, but I was wondering if our horses need to be wearing tack in the riding schools. If they don't need it, will wearing it help them in any way? Like gaining extra stats? Thanks!

they don't need it for the riding school.
i've not noticed a difference in earnings for tacked/untacked horses. sometimes tacked horses gain no stats and untacked gained 4+ stats

I was hoping that was the case. I just sent some horses without tack for the first time & then was wondering if I should have left their tack on. I'm relieved to know I didn't goof them up somehow. Thanks for the help, Kahzie!