If a mounted character's 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 attacking dice roll.
Because a mounted character has a height advantage over a character on foot, a mounted character gains a bonus of +2 on the attack dice roll if he/she is carrying out a melee attack. Hence, a good enough rider will benefit from fighting while mounted. This bonus applies whether the character is using his/her Riding or his/her relevant weapon skill in the dice roll.
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 attack modifier of +3 when wielded one-handed. On foot, Cogan has a basic value of 12 (= 5 + 3 1/2 + 1/2 + 3) when attacking 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 is 11 1/2 (= 2 + 1 + 1/2 + 3 +2 +2 +1) when attacking with the hand-&-half one-handed; the height advantage nearly makes up for his deficiencies as a rider.
There is a penalty of -2 on the attack dice roll if the character's mount is agitated.