2. As far as I can tell Olmstead kind of made this up by taking a bunch of different horse breeds and claiming they were all the same or speculating specific horses were Nesaean without direct evidence. Herodotus talks about horses bred in Nesaea. But he doesn't say this as if they're widely known. He explains the name as if he doesn't expect the reader to know what they are. (To my reading, the relevant fact is that the horses were Medean, meaning the dynasty before the Persians, and so a sign of legitimacy.)
The other citations are about horses with different names from nearby regions in Central Asia. For example, the War of the Heavenly Horses has no mention of Nesaea in any source and the reference to Plutarch, as far as I can tell, is entirely made up.
Separately, it's undoubtedly true that Central Asian horse breeders were (and are) very good and access to such horses was a key strategic resource for powers in the region.
2. As far as I can tell Olmstead kind of made this up by taking a bunch of different horse breeds and claiming they were all the same or speculating specific horses were Nesaean without direct evidence. Herodotus talks about horses bred in Nesaea. But he doesn't say this as if they're widely known. He explains the name as if he doesn't expect the reader to know what they are. (To my reading, the relevant fact is that the horses were Medean, meaning the dynasty before the Persians, and so a sign of legitimacy.)
The other citations are about horses with different names from nearby regions in Central Asia. For example, the War of the Heavenly Horses has no mention of Nesaea in any source and the reference to Plutarch, as far as I can tell, is entirely made up.
Separately, it's undoubtedly true that Central Asian horse breeders were (and are) very good and access to such horses was a key strategic resource for powers in the region.