How to get Epona with out racing?

No - the only way to get Epona is to do the race twice...

Enter the Ranch during the day and talk to Ingo. He will eventually ask you if you want to ride one of his "fine" horses for 10 Rupees for one minute. Say yes and then play Epona's Song and get up the horse that approaches you with A.

Once your one minute is up - Ingo will call you in. Pay him another 10 Rupees to ride again and do the same thing. Call Epona over and while you're on her -walk over to Ingo. He will ask if you want to race him with 50 Rupees on the line - say yes.

When riding the horse - you get 6 carrots which increase the horses speed when you hit A. The carrots will replenish after a few seconds if you don't hit A. Hitting A continuously doesn't make the horse get any faster - you must hit A when the horse begins to slow down. In order to jump fences - you have to make sure that you're not jumping them on an angle and you must hit A before the fence to get fast enough to make the jump. Make sure you stay as close as possible to the inside of the track - this makes for less distance in the end.

If Ingo tries to pass you - just cut him off - there's only one lap. Once you beat him the first time - he will give you the Rupees and ask you to race again - this time he will put Epona on the line (the dumb guy). After this race - he will keep his promise and give you Epona - but he won't let you leave the Ranch as he seals the doors! But you have the best jumper in the Ranch - so take Epona and speed her towards the gate to jump it and return to Hyrule Field for a well earned victory!

It cannot be done. Anyway when you are racing make sure you keep about two speed carrots so that you don't tire out.

You have to race but I can tell you that keeping on the inside of the racing ring and obstructing mr.ingo then you will easily win the race, allways keep atleast 1 carrot spare! Cya :P