If we have taken possession in any way (riding, leading or taken off the table by our warband) of a mount taken from any source (an enemy or an encounter), we keep it. I think all the rules say is that if a mount flees the table or is fleeing at the end of a game, it automatically comes back to its owner.
Our approach probably qualifies as a house rule, but no one has ever argued about it. Wagons have a rule for capturing I think (they got so many rules). Again it hasn't up (because our wagons are rare and defended by the maximum warriors who can possibly ride in them and the pesky owners rout before the possibility of capture.) If we did capture one, we would keep it.
If you haven't found any thing in the rules, I would ask the group.