Where are you located? That would make a big difference in price. For example, in my area, people often lend horses to friends, friends of friends, or other guests/potential members and are sometimes paid gas money. Sometimes the guest rider will give a gift card or some small amount of cash (like in a thank you card). But I’m in a area where our hunt consists of a small but passionate group of hunters so we are always eager to get new potential members to give it a try and there’s simply not a market for hiring horses out for hunts. However, some of my east coast friends have paid up to $200-300/horse/day to hire one for a hunt.
If someone rides one of my horses, I have them sign a basic liability release (for my state) and they sign our hunt’s release. I have been advised (by horse professionals in my area - haven’t looked into it myself) that if I were to start charging for use of a hunt horse that I might need a different type of release form. I have my guest riders either tack up the horse themselves (and then I check it all) or I tack up the horse (and they check it) to double check everything is in good repair and adjusted correctly. Honestly, I do worry about the liability, but I’ve had so many people be kind to be with regards to lending horses that I feel like it is important to pay it forward now that I’ve got a couple of nice and easy ones 
Just out of curiosity, how does a hunt without hounds work?