I know that mounts are mentioned in the rules book, in passing, when discussing the stats for a Hare. No mechanics are given in the core book. Have errata/clarifications/add-ons been produced? Either 1st party or 3rd party in origin. Would it be hard to add in?
There are official rules for it in the boxed set's rules expansion booklet. It's supposed to be made available in PDF eventually; I don't know if it is yet. (Luke Crane mentioned the plan for a PDF version of the expansion on the BurningWheel.org forums.)