I have not experimented with this tactic yet, but last night playing the Seleucids, I noticed that chariots showed good potential at chasing down horse archers.

One common problem I have had with chariots is that they sometimes will run amok as soon as the battle starts--before any enemy contact has been made or is even imminent. Seems like a bug. This happens typically to chariot units that are depleted in number from a previous battle. It's turned me off to using chariots very much, and now when I do, I treat them as expendable and charge them at something far away from my battle line and let them fight until dead or routed.