When you first start out in Fallen Earth, after a couple of quests, you get given a Horse Shoe which can be found in your bag. (i key) You either double click this once outside the LifeNet station, or right click and select use. This puts a Horse (Old Nag) close by to you. To mount the horse you hover your mouse over the back of the horse, and left click.. Please note you can also press the 'Y' key to interact with the horse.
Your horse will have a stamina bar of 8000, which reduces each time you ride it, once it hits 0, your horse will begin a slow trot. You need to make sure you have 'Horse feed' in your bag to feed the horse, to make its stamina get back to 8000. You can purchase more feed from a Horse merchant, found in most towns, and indicated on the mini map with a green horse shoe.
Later on when you get your nature skill up, you can craft your own horses, which do have more stamina. The next one up to the Old Nag, gives you 16000 stamina, and 8 inventory slots. The inventory slots can be found on the small i button on the horses status bar, which appears when you are close or on your horse.
The next one up to that gives you 24000 stamina and 16 inventory slots. Just remember, to always carry food with you, to feed those poor neddys.
If you lose your horse, after death.. or simply loosing your way.. you have 2 choices. You can run to your horse on foot, by following the small icon on your map. Or you can go to a stable manager, and tow your horse back and park it, then bring it back out. After a while, or after a few hits, you may find your horse is damaged the 100/100 bar above the stamina bar, if this happens you need to have a vetinary kit in your bag, then click on the heal button on the horse status bar.
If you want to add to this page, or make changes, please feel free. Thanks for reading.
Also if this page has been done before, I hope ive added a few little bits to making it clear. Don't want to step on peoples toes!