Questions about horses have been asked and sometimes answered. The attached is an attempt to more thoroughly address those questions, plus more information than most people would ever want about the LoTR horses.
I would vote for the Lusitano (PSL) rather than the Andalusian as the Mearas. They are not all that different that it matters too much, but it is first and foremost the Veiga line of the Lusitano that are breed for bullfighting. Still, I would be happy to say "Iberian" (and include both PRE and PSL). Of course I might be a little bit biased since one of my horses is a Lusitano-mix...
A lagre Throughbreed would also work for Shadowfax, I think. The lager, older type of race-horse (like Man-of-War) would fit the build.
Asfaloth as an Arab I would totaly buy. The lighter horse seems to fit well the description.