So far as I can tell (DMG 46 Encounters with PC Mounts is key), both pixie and mount get turns, both can use move actions to take advantage of the mount's move speed, and the mount gets to use the pixie's skill check bonuses but not take advantage of, for example, feats that let the pixie re-roll Acrobatics.
@BrianBallsun-Stanton Yeah, but that's not needed to ride a creature like a mount, it just means the PC doesn't have mount traits or powers the pixie can take advantage of with the Mounted Combat feat.
@BrianBallsun-Stanton All I can find is three insufficient and speculative paragraphs on DMG 46 that don't tell me if they overrule the standard mount rules or simply coexist with them.
@BESW This doesn't sound quite right to me. I would suggest that they have to share the movement ie. the pair can only move in one or the other of the players turns.
Also, I'm very thankful the pixie isn't a paladin: Holy Steed Benefit: While you are mounted, your mount gains a +2 bonus to all defenses and a bonus to damage rolls equal to your Charisma modifier.
@BrianBallsun-Stanton That's a good place to start, cool.
It's not move actions all the way down. The pixie don't grant the gnome a move action he can use to grant the gnoll a move action to make the horse move.
If the pixie tried to use his move action on the Tower O' Heroes, you'd wind up with a faceplanted gnome, an irritated pixie, a laughing gnoll, and a spooked horse.