Yes, horses are purchased so you get to keep them and use them all the time. When you summon your horse, it can be ridden for 24 hours or until you dismiss it.
There is no refresh timer on a horse so if you wanted to, you could summon then dismiss and then re-summon all together, with no penalty and no waiting.
The horse itself is actually just a whistle that goes in one of your character's two activatable slots. Click on the whistle, (I keep mine down in one of my hot bars), and you cast the summoning spell.
Yes, you can fight from horseback and IMHO, it is very cool looking. If I am soloing my warden, I never leave horseback unless I need to go for a swim. When grouped, I tend to ride if everyone else is and dismiss if one or more group members are without mounts. (Horses are so much faster than running that you will leave unmounted group members in the dust when you travel.) I don't see any penalty from fighting on horseback but a monk friend of mine claims he doesn't do as much damage when mounted.
Now the downside... first, horses are
VERY expensive so it's not something that you could afford with a low level first character. Even if you are in a guild and buy one with personal status points (guild experience), you are looking at well over one platinum in cash plus the PSP for the lowest level horse available.
(The exception to this is the level 20 fluff spell for Pallys and SKs. For a few silver, this spell will grant you a nice looking mount with a 10% speed increase. The hook is that you can only do this if you are a lvl 20 Paladin or Shadow Knight.)
Second, horses are no-trade meaning that the person who buys the horse is the only person who can ever ride it. If you want to "trade up", to a better quality of horse, you can re-sell it to the stable where you bought it, but you can never sell it to another player.
And third, they cannot be ridden into the water. If you attempt to cross a river, lake, or enter the ocean, the horse will un-summon automatically. Not a big deal but something to be aware of.
On the plus side, the horse never needs to be fed or watered, never takes damage. and does not react to battle in any way. In addition, I think they have really cool annimations and make great sounds. They also look really neat when you "jump" them over an object.
One last thing, you can't ride a horse in any of the "home" villages. There must be an ordinance against it! This keeps horses out of the banks, (which was always a problem in EQ). You can however ride in Queynos and Freeport proper and of course, you can ride in any combat zone.
There is a great article showing what all the different horses look like, what the different speed boosts are and how much they cost. It is located
HERE Good luck and happy trails...