Druid with mounted combat or an oracle with the nature mystery for a very very intelligent horse. Both have a 3/4's bab which isn't that bad, and are full casters. Mounted casting does get the short end of the stick as it's relatively impractical for most campaigns. Maybe ride-by attack so you can some hit and runs.
There are two mounted fighter archetypes. What I would suggest is roughrider fighter 5/nature oracle x (or druid x)with boon companion.
That way you can make best use of the roughrider's abilities while still getting some spellcasting in.
If you can be an aasimar you can take the celestial servant feat to buff your mount even further.
If you want to be a legit Cossack, you could just go around beating nonviolent protesters to enforce a ban against demonstrating against your code/king/religion.
In more serious terms, you'd need to have decent concentration to not fizzle from casting while riding, I think. That might be a rough hurdle if you do intend to multiclass.