As usual the quest is utterly confusing and frustrating.

After getting the quest, the timer starts immediately.  So you try getting on the horse next to you.  NONE OF THEM ARE THE RIGHT HORSE.  If you were like me, you wasted valuable quest time figuring this out (because the quest doesn't tell you that, it's rigged to make you fail.)

You must run down to the other set of horses that are SE of your position.  One of them is the right one.  Then head due south and that's the first gate.  Now watch your arrows for the other gates because there isn't a clear path to them.  Sometimes the gate in front of you is the wrong gate.  I found that out by following the path, which caused a failure.  And the previous poster is correct, do not do this at night. 

The first gates are pretty uneventful, just follow the path south directly out of the stable. Towards the end you'll need to cut through fields and jump a lot of fences to make it in time. All shortcuts will be to the inside of the track. Don't run through water, and don't jump off any cliffs.

When you past the last gate, stop and do NOT breathe a sigh of relief, the clock is still ticking. Right in front of you is Eogar, the questgiver. You must talk to him before the timer runs out.

Congrats. You now have the ride skill!

Directions

The course basically goes in an anti-clockwise direction and returns to the stable yard.

Hint: don't do this at night - the gates are too hard to see. Wait for daylight.