Basically, here's how it breaks down:
Jagen - Paladin
Cain - Chevalier (Sword)
Abel - Vanguard (Lance)
You get three to start with right off the bat (as is traditionally done ever since).
Hardin - Cavalier (Sword/Lance) - psuedo-Lord promotes to Master Knight
Wolf - Ranger (Bow/Sword)
Then you get to choose one of his guards to join the party.
Edwyn - Mage Knight
Rasha - Cohort (Axe) - Replacing Roshea's role, a Cavalier
Vyland - Soldier - Reclassed from Cavalier
If we're counting Troubadours, I added one of those too.
Maria - Troubadour - Reclassed from Cleric
There's two Archanean mounted units.
Midia - Valkyrja (Axe/Staff) - Reclassed from Paladin
Horace - Cataphract (Sword/Axe) - Reclassed from General
And one final cav back in Altea (Marth's homeland), you get one of the two based on whether you completed a series of events leading up to the jointime.
Arran - Paladin
Frey - Vanguard
That's nine/ten mounted units, based on player choice elements. Originally FE1 threw you: 8 Cavs/Paladins, 2 Rangers. The difference is in the diversification of the units. FE6 is the series' high-water mark with 12 mounted units, FE9 is the low-mark with only 6. True, I didn't really cut down on "cav bloat" but rather tackled "cav redundancies." Hopefully the number of mounted units isn't terribly overbearing: 10/52.