About a month ago i've tried it,without a saddle,and while the horse just walking. I used a 70cm (27") sling and a helicopter style. Just as you would think,it feels awkward and week. Also you cannot sling on the right if your right handed.Using a saddle would probably improve on the case,but dunno how much.The horse did a small jump the first time  i've slung,but i was expecting it.The horse could well tolerate the sound with a bit of practice.The power of shots is considerably less than on foot,as you cannot use your body,again a saddle would probably help.Also i imagine that a good rider and slinger might be able to use the horses movement to get more power in his shots.When the horse lands on his front feet in gallop the slinger could whip his upper body into the throw.Like horsearchers loose the arrow while all the feet of the horse are in the air.A well trained slinger who knows to ride very well and using a saddle could be effective,but a good horse archer would beat him easily in performance. I'm definitely going to try it some more.  
There is one painting from a greek vase depincting schythian mounted slingers..as it was written where i've found the picture.It was already posted somewhere around the forum.Also it says that the horses are dressed like sacred ibex.

Maybe the horse provides additional speed?
Greetings,
Mauro.

I think those "Scythians" are in fact riding ibexes, so it's a fantasy image (like pygmies fighting cranes).  
 
The Romans slung on horseback. But then they really, really liked to throw things from horseback, with great accuracy (they had exercizes to practice deflection shooting and even throwing javelins backwards, iirc). The question is whether this is just one of the weird things they did, or if they picked it up from other people (one of the exercizes they had was "horse tricks that other peoples e.g. Germans are good at", i.e they deliberately set aside time to try and imitate tricks they saw other peoples perform).

I think that if a mounted slinger could get his timing right, then he could send massed fire towards enemy lines. nothing accurate mind, but definitely in the right direction. What's more, the slinger and horse could carry slightly more armor and a lot more ammo, making them more efficient against archers. It would allow them to carry armor to deflect arrows, and a lot more ammo, as they probably will need if they're slinging off such an unstable platform. But then they could get in a lot closer to archers, without going to close.

Quote from Liberty dog on Mar 23^rd, 2012, 11:31pm:

 
Been there, done that, nearly broke something. It's hard to load, sling, and balance. Reloading requires two hands, so you have to ride the bike with no hands, while trying to stick a stone in a sling without dropping it. If you can figure it then it would be awesome.

The picture could very well be a mythical portrait as thearos wrote,but as crazy the ancients were i could imagine them even riding ibexes while slinging around..now that would be the show Mounted slingers were probably rare,let alone ibex riding slingers,but i'm sure it was done to some scale. I can imagine this in deep into the history,probably soon after man started to ride horses.

Quote from Mauro Fiorentini on Mar 22^nd, 2012, 9:42am:

Yep, how could one forget her.  Apparently she only shot a bow from her horse.  I love that shaggy horse she's shooting from. It's almost as pretty as she is.

She is very cool. I hope she comes back.