My advice......and realize that I am no lover of the equine, but have had some experience "renting" horses for elk hunting......
If I didn't have my own horses or know someone that did, I wouldn't do what you are talking about doing!
Just my two cents worth. If you know anything about horses, you know that you don't know anything about the ones someone is "renting" you!!!! You never know how your own horsewill act in strange environments, let along someone elses. Seen some gentle Texas steeds be nothing but trouble when trying to make them into Rocky Mountain horses!
My last word of caution is that if you do go ahead with your plan and you are lucky enough to harvest an elk, be warned that a lot of horses don't like the smell of blood/elk carcass and sure ain't about to let you put it on their back. If you are renting from a reputable bunch, make sure and ask about the experience of the animals you are getting. They may seem like horses from heaven when starting out, but once you get back to where you are going, if they change they can ruin your hunt.....period.