Hi Louie,
There are a couple of mentions of riders with bows. When they are first encountered by Aragorn, Gimli and Legolas 'A thicket of spears pointed towards the strangers: and some of the horsemen had bows in hand, and their arrows were already fitted to the string'. And when the Riders trap the Uruk Hai near Fangorn 'a few of the riders appeared to be bowmen, skilled at shooting from a running horse'. But when we finally see the Rohirrim charge at the Pelennor Fields the description appears to suggest a force of all heavy cavalry.
My take would be that the Riders of Rohan are heavy cavalry, but a few happen to have brought bows with them on campaign. From memory, there's also mention of mounted archers in Unfinished Tales (sorry, I don't have my copy to hand), but I had the impression that these were archers who happened to be on horseback to keep up with the glory boys rather than dedicated horse archers per se.