Societies do not maintain unusually large cavalry forces where there is not an underlying social and economic basis for widespread horse-use. The exeptional cavalry content of Rohanic armies, I would emphatically assert, must represent some peculiarity in the economic and social make up of Rohan relative to Gondor. The movements need not, if the pasturage was of reasonable quality, have covered huge distances. Indeed a particular herd could have been centred on a single fixed settlement where a proportion of the stock could be over-wintered. This type of economy would still have entailed that a proportion of the adult male population move with the herds and therby ensure that horsemanship and horse-ownership would be at a premium.
History shows that the two are by no means mutually exclusive.
The Mongols in the time of the successors of Genghis had Karakorum as a capital. Further, that the presence of fixed settlements of varying size does not preclude this type of society.