We have a similar situation at our farm... partial self care, they feed, but you handle what kind, how much, worming, vet, and farrier.
The concerned owners got together with the vet, decided on a schedule for type of worming, and then agreed that when board was due, you wormed your horse. We posted it with the barn rules and generally don't have an issue.
If your horse says no, you either asked the wrong question or asked the question wrong
And God took a handful of southerly wind, blew His breath over it and created the horse