I've been experiencing this problem since I hit level 7. I am now level 21. So here are the repro steps:
1) Login to level 21 Wood Elf Ranger.
2) Stand anywhere that you can ride a mount - where the picture above "7" lights up.
3) Hit "7" on the keyboard.
4) Mount appears. You get on.
5) Mount disappears instantly in a puff of smoke/cloud. You fall down.
I have tried resetting everything in the game. The only thing I haven't done is uninstall the game and reinstall. I really would like to be able to ride any of the 3 horses the game has given me. Anyone have any advice?