This is based on a code found by Vampire Arthur which basically says to go to Lon Lon ranch without Epona, call epona, go in a door, and when you go back out Epona will be stuck below the ground. Click here for the full article and screenshots on The Odyssey of Hyrule. But many gamers have had problems with the glitch (including myself) so I decided to launch a full investigation into the cause. What I found was that the glitch is much more complex than what was explained. Thanks to Art for bringing this to everyone's attention. What is on this page is an extension of his glitch with all new locations I have found it to work.
First, you should realize that there is some kind of link between all the locations you can ride Epona in the game. If you go forward on Epona in one place you will also go forward with Epona in another but usually in a different direction on the map. However, there are specific locations that you have to be at for it to work. The glitches occur because by doing this you can put Epona through walls, above water, and below the ground in the corresponding location. I have been able to see Epona under these strange circumstances in 3 places: Lon Lon Ranch, Gerudo Valley, and Gerudo Fortress. The reason that it Epona is not at (or hard to find at) Lake Hylia is because she could easily be put above water and be forced above the limits too high to be seen. In Hyrule Field she is probably below one of the many hills. The first logical place to begin is to explain exactly how you can do the original code found by Art.
First, get off of Epona halfway up the ramp connecting the bridge at Gerudo Valley to the ground. Go to Lon Lon Ranch (without Epona) and play Epona's song when you get there. Then go in a building and exit back to the ranch. Epona will appear below the ground. You can change how far in the ground she is by changing the elevation you are at on the bridge.
At this point I should note that your height really only matters if you want to be seen below the ground or end up above water. If your original height is higher you will not float in the sky if you are above land. Also, the trick works whenever the screen is refreshed either by exiting and reentering the screen or else by playing the sun's song to refresh the screen (only works at Gerudo Fortress and Lon Lon Ranch.) Here are the other locations I've found for similar glitches to work:
Epona Floating Above Gerudo Valley
Go to Gerudo Fortress and go past the wandering Gerudos. Go a little over 3/4ths of the way up the hill before the first corner with the wall. (Start at the corner Epona can fall off of. The starting point is as close as you can get to the entrance and be on the higher hill.) Make sure you are right next to the wall when you dismount. Get off of Epona there and go to Gerudo Valley. Play Epona's song, go in the tent, and exit back to Gerudo Valley. If done right you can look up and see Epona floating above the river. If you go to Lon Lon ranch and are about the length of 2 Eponas east of the highest fence in the enclosed area and then do the trick at Gerudo valley Epona will also float above the water but will be at a lower elevation.
These shots Code Gamer X took show the height you will be if you do the trick starting at Lon Lon ranch. Click them to see their full size.
Get Inside the Tent
Go to the right side of the tent and get as close to it as you can facing it head on (the water should be directly behind you.) Get off of Epona and go to Gerudo Valley. Play Epona's Song and then the sun's song to refresh the screen (or exit and return.) Get on Epona and move forward slightly. Get off and go to Gerudo Valley. Play Epona's Song and enter the tent. When you exit Epona should be halfway in the right side of the tent. Push A to get on her and you should be inside the tent's polygons (the game won't switch to the screen with the runner and carpenters.) You still cannot enter the tent easily on Epona even though you can try going to the entrance from the inside.
Sarge took these screenshots with Epona in the tent.
Behind the Fortress Wall
Get off of Epona by the rocks between the water and the tent. Now go to the Gerudo Fortress, play Epona's song, and reload the screen. Depending on your exact location Epona will probably be behind the wall or halfway sticking out of the wall. You can push A to mount Epona in the wall. If you do this and then use the bow the camera angle will become messed up. Also, if you want to see Epona behind the wall you can charge up your sword (sorry, you must momentarily part with swordless Link.)
These pics were taken by Code Gamer X and show Epona behind the wall at Gerudo Fortress. Click them to enlarge.
That's all for now. However, I believe this may have only scratched the surface. I haven't yet tried to see if Epona is below the ground at Hyrule Field by doing swordless Link and haven't tested many other possible scenarios. If you find out anything else that can be done with this please send it in and of course you will receive full credit.