[samrohan]

You guys seem to forget two important links between horses and elves in the book.
Firstly, Glorfindel at the ford tells his horse to carry Frodo to Rivendell in Elfic and secondly Legolas not only is accustomed to riding but the meara (whose name I can't remember) he rides is able to having elves ride bare-back on him.
To me, these two points clearly put the link between the Mearas and the Elves far back in time and my guess is that like the Ents were brought to life by Elves, the Mearas or horses in general in Middle Earth were kept at an early age and extensively used by the Elves.

Lothlorien most certainly had horses, though not described in so obvious ways in the book, while Mirkwood must have used them too as Legolas is obviously a good horseman.

The horses in Mirkwood must only have been used for far journeys outside the woods, this due to the dense forest.

Other than that, horses in Middle Earth were as wide spread and diverse as on our Earth. A majority of races have and use them and some have no need for them.