McCormick's Creek State Park and Brown County State Park both offer horseback riding opportunities. Other parks have horse trails but not rentals.
McCormick's Creek in Spencer is the only one I know of. Brown County has one but not a fan.
I believe Brown county (which I think is closed for a bit due to flooding) is the only park to still offer horseback riding.
I'm assuming you mean horse back riding, but I am not aware of any. It was expensive when they did offer it..
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