Hi there, my daughter also loves horses. She is now 6 1/2. I tried to find her a riding program (English) when she was 4 and was told she was too young by every place I called in Dallas. We are from the Northeast and found a place for her to ride at while we were visiting one summer.
I finally talked an instructor into take her on as a private student when she was 5 1/2. She LOVES it and now rides once a week. I think the average start age for most riders here in Dallas is 7-8 years old.
You may have more luck looking for farms to visit if you just want to do pony rides. Pure equestrian centers will most likely say your daughter is too young.
Good luck! There are a lot great places to ride in the area....