Cavalry riders can choose to shoot their personal arms using their BS. All the normal rules apply so if the entire unit remains stationary they can use rapid fire weapons carried by the riders at full effect. Heavy weapons cannot be fired by moving cavalry, but may be fired if the unit is stationary (it can be imagined that the riders dismount to fire while they are halted).
Cavalry Shooting
Source: Core Rulebook 3E, p. 93
Cavalry riders shoot using their BS and can fire rapid fire weapons at full effect if stationary, but heavy weapons only if the unit does not move.