RE: Carrying a bow on horseback?
It is almost impossible to tie on a bow hard case on a saddle. And in fact it becomes almost dangerous for the rider. Maybe someone has a trick on making this work but never have we got it to work well. Cabelas has a new bow back pack now. I'm not sure yet if you could sit a horse with this on. I will personally try it out this year.
The best thing we have found is parachute cord. You tie a loop just below the grip on your bow and sling it over your shoulder that way. And when shooting the cord is hanging below your grip and completely out of the way.
The reason the outfitter refused was because of safety reason. Most people are not adapt to getting off and on a horse and that big case that won't move when getting on or off causes alot of people to fall off. And no outfitter wants a client with a broken arm or worse. Its safety and that's why he refused.