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You can only get her after the 2nd temple, because you need a Powder Keg to destroy the huge boulder at Milk Road. You need to talk to the little girl (Romani) and play her target shooting game. After you win the game she'll teach you Epona's song and you can ride Epona whenever you want from now on !!

You have to destroy the boulder and get into Milk Road on the first day though, otherwise Romani will be gone.

^ You need a liscense for a powder keg first. If you go on the third day she will be there but won't give you Epona ( maybe from the ali- wait spoilers) on the 2nd one she wont be there ( unless you help her with her favor)