I’m a morning person, so I’m very sympathetic to the OP–it would drive me crazy, especially in the summer, not being able to ride until the sun was up and the best part of the day exercise-wise, was gone. Most barns I rode at, however, didn’t allow for before-work-hours riding. Often, the trainers were riding the horses in training during the earliest “best” hours and didn’t want boarders/lessons clogging up the space. I think the earliest hours barns allowed riding was 7:30am-8:30am at the barns I’d ridden at. Sometimes it was also because the owner lived on property and didn’t want people on their property that early, as well as the worker schedules @beowulf referred to above.
At a barn where I was just taking lessons, one trainer who said she wasn’t a morning person didn’t start lessons until around noon, every day, except on Saturday. This was really annoying in the summer, since it meant the entire lesson was devoted to managing the heat in a way that it wouldn’t have been earlier, and it’s certainly better for the horses to work during the cooler parts of the day.
But all the OP can do is ask and see–ultimately, however, barns are a business, and all have different degrees of flexibility, depending on size/ formality. I can definitely understand why barns don’t want boarders feeding hay, though, just based on personal observations! (Especially if there’s different kinds of hay available.)