I have. It’s actually pretty common
I’ve also seen ‘barn trainers’ especially - not independent floaters, but one managing everyone in the same barn - tell their group to buy the protective boots they are endorsing. Or something else that’s noticeable to spectators at a horse show as a particular brand. It’s one of the things a trainer will assure a prospective sponsor they will do. The students may or may not come through, of course.
Saddles would not surprise me at all. Even girths, breastplates, bridles. It’s all brandable, advertised to be recognizable. Spectators and browsers of photos will notice it.
Sounds normal
Older horses need that help
They may need that help, but the charges for it should have been disclosed as part of the lease agreement, and not tacked on after the fact without as much as a discussion.