Chance, Hay is a staple of any horse's diet and is necessary. You'll find that if you cheat and remove it from a horse's diet you will open youself up to a world of possible health issues. Hay prices will vary, quality will also vary. There are different grasses to consider, each breed is different in their needs. The one size fits all approach does not work with equines. Some are "hard keepers" meaning you will need hay, grain, supplements, etc to keep them at an ideal weight and you will find the combos necessary add up quickly!
If considering a horse please do some research. Find someone willing to teach you what they know, visit and help out for a few weeks. Learn about routine care, diet, cleaning, grooming, vet care, issues to watch for and safety. Talk with a vet and get a good firm grip on the costs involved, trust me an accident can shock you silly, vet costs are inevitable. Farrier costs also. I have had several friends that were interested in getting a horse for a child. I talked them into spending a week with me learning and 9 times out of 10 they decide there is too much work and cost involved. Horse ownership is fun and rewarding but a big commitment! When I adopt an animal it is for the life span of the animal! You can never ask a bad question nor learn too much!