Other Mearas?

[Firefoot]

Yes, only the Rohirrim had Mearas. The first was Felaróf, who was Eorl's horse. Eorl's father was trying to ride Felaróf and died when he was thrown, so Eorl demanded that Felaróf allow him to ride him as weregild. The Mearas were Felaróf's descendants. Until Gandalf, they would allow no others than the Kings of the Mark and their sons to ride them. Therefore, Snowmane was one of the Mearas, but Éomer's horse Firefoot (that's me ) wasn't. They were long-lived, living as long as men, and very valiant and strong.

And as to your second question, the answer is in Aragorn, Legolas, and Gimli's first conversation with Éomer:

"Then you do not pay tribute to Sauron?" asked Gimli.
"We do not and we never have," said Éomer with a flash in his eyes. "though it comes to my ears that that lie has been told. Some years ago the Lord of the Black Land wished to purchase horses of us at great price, but we refused him, for he puts beasts to evil use. Then he sent plundering Orcs, and thy carry off what they can, choosing always the black horses: few of these now are left. For that reason our feud with the Orcs is bitter."