I still think that most specialized classes should be Prestige Classes.
If you make Beast Rider a Prestige class instead of a regular class it will help offset the power some.
Make some of the mounted feats prerequisits to the class. For instance the Halfling Outrider (Sword & Fist) needs to have Mounted Combat and Mounted Archery before they can take the class. Windrider (Masters of the Wild) is another good class to look at for ideas.
The same with the Archer Class (Deepwoods Sniper, Arcane Archer, and Order of the Bow) just take the best features of these classes and combine them...