A linebattle is not decided by the cavalry, even if they can shoot from horseback.
The number of cav players is very small because the server admin mostly dosent allow large cav detachments during an event.
Its not that easy to shoot someone from horseback even he is in cover and you are under fire by his reg.
And I also think that most of the Infantry Regiments are able to handle cav who shoots from horseback.
My solution: I think cav should be able to shoot and reload from horseback, but they should have less accuracy and a long reloading time (maybe longer than muskets event it its unrealistic). The rest will be done by the rules during the events (like no pistol shooting from horseback for Colonels which is REALLY ******* OP).
But at least it dosent matter which solution you choose:
It will be fair anyways because in most battles both sides uses cav wich have to use and follow the same rules.
PS: sorry for my bad english 
Cavalry can be a critical component for Victory. When used right. Each event has their own rules but for the Saturday LB that I host, all I ask is that both sides have equal numbers of Cav and no more than 15ish players. 15 is actually quite a lot considering that is 15% per side...
As for shooting, depends how good you are, I managed to headshot someone whilst mounted before - its on one of the vids, and was very fun. Never done it again apart from executing someone though haha.
Actually no, most of the Infantry Officers complain no end about cav firing from horseback, its why the DA and UA has to put in the rule back in 2012 - the officer meeting would just be a bunch of whining infantry officers. Nowadays its different as many regiments have come and gone, and thankfully in the DA event at least, the Infantry Officers dont QQ about it.
But another problem was the Artillery, unless they have Guards they are under serious threat from Fire from Horseback as their anti-cav squares wont stop a bullet fired from elevation. There have been some complaints but I would say its the job of the cav to stop the enemy cav reaching the artillery, or for the arty to have guards. Again, we have been way too restrictive on Cavalry for almost the entire duration of my play time.
The current system of forcing them to dismount to reload is fine as is. It means they get one shot from horseback then they go melee until they can safely dismount and reload. Its fine.
The main problem with Cavalry, is the sheer unbalance in favour of the Union side cavalry. And yes I am talking about the stats.
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