Not really. Horses might be faster than men but they are bigger thus easier to hit with arrows.
I thought the system was more of rock-paper-scissor. Inf<Cav, Cav<Arc, Arc<Inf. Something like that.
Speed is a vital part of evasion of missle weapons, especially in the cases of volleys. The idea is to speed through the target zone, reduce the amount of volleys you face and thus arrive at your target with the larger part of your forces intact.
http://www.bbc.co.uk/news/10302388
I think it is depend on the breed. Like mongolian horses they are not as fast as other bigger horses but they could run longer and didn't get tired so easily.
Larger warhorse were actually quite slow in comparison to some of the really fast breeds. The important thing was they could carry the fully armored knight, and also their immense weight increased the impact force of the charge.
The problem with Cav is that is a large category. Horse armies like the Mongols and some of the eastern empires the Roman faced were incredibly mobile at the strategic level due to the way they used light cavalry. When you think of typical medieval cavalry though the image is medium or heavy cavalry. The nature of these breeds increased the load on the baggage trains, they required reasonably large amounts of decent feed to be in top shape, where other light cavalry horse could rely on grazing to a much greater extent.
