New Lotro expansion Siege of Mirkwood will bring more functionality to Lotro mounts.
No longer will they simply move players around the game world quickly. With Siege of Mirkwood you can talk to an NPC on your mount, buy stuff from a vendor, cross land block boundaries, enter large spaces on horse without dismounting, emote on your horse, you can even name your horse. [source]
Mounts are being changed over to skills, not items. This means you will no longer be required to carry a mount in your inventory. In your skills panel, there will be a "mount" tab, which will list your current stable of mounts -- your horse, your other horse, your goat. And, because of mounts becoming skills, a number of issues with mounts will simply cease to exist: You will now be able to pass into instances and new zones while on your mount; you can now interact with NPCs (including vendors) from your mount; and you can now use emotes (with complete animations) on your mount. In other mount news, there's a brand new goat, the Wild Goat." [source]
You can have multiple horses. Each is a seperate skill, but there is no limit I am aware of on the number you can have. There will be a Dev Diary on the new system, so that should give you a ton of info when it's published. [source]