Rent a horse and wander on your own? Yeah, no. I agree that isn't likely. But guided trail rides should be an option.Around Edmonton the challenge is finding a day/trail ride I think. Most horses are privately owned or you're part of an equestrian club. Obviously most places aren't going to just let you rent a horse and wander around on your own (the liability would be crazy I assume).
That being said I'm sure there's something within an hour or so drive.