A few things, first Iran and Anatolia, while both being mountainous and having hilly terrain also have areas that are exceedingly flat and excellent for cavalry.

Second, that depends on how cavalry is being used and what their role is in the army. The primary problem with mountainous and hilly terrain is that it greatly restricts two of their best traits, mobility and maneuverability. However, while the terrain greatly dictates the ability of cavalry to operate it does not mean that generals had no uses for cavalry in such terrain or that cavalry could not fulfill arguably their most important role which was scouting and screening the main body.

Third, remember that there are very different types of cavalry and the uses for them vary. European heavy cavalry are very different from the lighter and more auxiliary cavalry units of Iran or Anatolia. This isn't to say they didn't have their own heavy cavalry variants, but for the most part the nations you're speaking of were using far lighter cavalry who were more diverse in the roles they could take and play during a battle.