A light cavalry archer is easy enough to accommodate. A Human (which someone from Rohan would be, obviously) can begin play knowing the feats "Mounted Combat" and "Mounted Archery". It's possible to specialise further in archery as you progress. Alternatively, you could pay more attention to your
archery at the start, with a view to factoring in the
mounted part later. You can build this onto the standard fighter chassis and still keep enough all-round ability to be useful when you're not on your horse or the circumstances don't suit archery. As I said to
glee, any amount of assistance is available on request.