: I don't claim to be an expert in ancient military tactics, but can see that mounted horsemen must have some advantage. By moving quickly they can reduce the risk of being hit themselves, and can even drive their foes to desperation by circling around them (Indian style). If the enemy has only few archers, the other soldiers can do parctically nothing except pray they won't be hit.
: Archery appears to have been common in ME, even among the Orcs. A band of mounted Orcs could have been totally murderous (any ideas why Sauron never resorted to this?). This may be a reason that dwarves, for example, who are not recorded as having made use of archers, were forced to perfection their armour technique (mail shirts etc) to compensate.
: Mounted cavalary, however, does have one drawback. Horses are expensive to rear and feed. This is why they were especially common in places like Rohan which had exceptionally fertile soil. Many other nations probably wouldn't have been able to afford an army of that type. Applying this to the Dunedain of the North, their horses suggest a certain degree of affluence, which means their homesteads cannot have been of the simplest type.

But archery has great advantages whether mounted on horseback or not. It would be especially advantagious for a smaller group (such as the Dunadain) fighting a much larger one (like an army of orcs).

Firstly, you do not have to get close to your enemy as you would have to in a sword fight or such-like. This gives smaller armies the advantage as they may kill/injure many foes, while hiding at a distance, without risking themselves.

Secondly, in comparison to the javelin or the spear, the arrow can be shot from a much farther distance with far more accuracy. Even a badly made bow can shoot an arrow twice or three times farther than a spear with more accuracy. The bow and arrow also places less emphasis on size & strength of the person wielding it (which would be considerabely more important when in a sword fight or throwing a spear) thus a small man or even a small boy would be just as likely to dispose of his foe as a great, big man as long as the skill level is the same.

Then their is fact that bows & arrows are easy to make and at small expense whereas swords spears etc take much longer to make and at a much higher price. The spear, of course, is lost as soon as it is released whereas a bow is a constant companion and arrows can be many and easy to make.

When mounted you have the added advantage of speed and others that you've listed above.

It is no suprize then that the Dunadain and the Rohirrim were skilled archers. It would have advantaged them greatly as they were outnumbered by their enemies most of the time.