RAW? Nope.
Not RAW? Create a feat called "Mount Companion". Your companion is now Large, and you can ride it. Since being Large provides no inherent benefit (as it did in 3e), aside from taking up 4 squares, that's all there is to it.
As for leveling up: anyone thought of including a mount in the party XP division and leveling it up? So your Warhorse (Brute 3) would remain 3rd level until you reach 3rd, and then get a share of XP to level up alongside the party. Optionally, at 10th level you could even take another feat (say, "Celestial Mount") and turn your warhorse into a Celestial Charger.