A mounted character can block normally. If a mounted character chooses to parry, he/she does not move on the combat board; instead, he/she has to maneuver in the saddle/vehicle and so has to make a dice roll to remain mounted (counts as overcoming an easy obstacle).
When a mounted character blocks or parries, if his/her Riding (including relevant specialisms) is lower than his/her relevant weapon skill (based on weapon used), his/her Riding (including relevant specialisms) is used instead of his/her relevant weapon skill in the defence dice roll. There is a penalty of -2 on the defence dice roll if the character's mount is agitated.
For example, Cogan the barbarian has a Melee skill score of 5 with a +3 1/2 points of specialism bonuses in fighting with a hand-&-half, a Riding skill score of 2 with a +1 specialism in riding horses, and a CO score of +1/2. The hand-&-half has a weapon parry modifier of +2 when wielded one-handed, and a parry maneuver gives a +3 bonus. On foot, Cogan has a basic value of 14 (= 5 + 3 1/2 + 1/2 + 2 + 3) when parrying with the hand-&-half one-handed; when riding a horse (in this case, a warhorse (+2 bonus to Riding dice rolls) equipped with saddle, harness, reins and stirrups (+1 bonus to Riding dice rolls)), Cogan is less comfortable, and his basic value when parrying is 11 1/2 (= 2 + 1 + 1/2 + 2 +3 +2 +1) when parrying with the hand-&-half one-handed; he will also have to make a Riding dice roll to avoid falling off his horse.