Trying to build a horse emblem

I'd probably exchange mathilda for Camus and remove frederick for brave lyn, elise or Reinhardt.

On the other hand, Cecilia with Gronnblade will be your nuke and sweeper.

Nothing wrong with any of the units you suggested there, but when people build horse teams usually it's mages, B.Lyn, and 1 or at most 2 melee units who serve mainly as tanks and colour coverage. The idea is that horses have a lot of mobility, and ranged horses cover practically the whole map plus they're really hard to block because...well...they're ranged units and will fire over a front line to units behind. The style is generally very aggressive and kind of brutish, just grotesque amounts of firepower, +24 buffs to blade tomes, blast the living daylights out of everything.

Ares is probably the main unit of your initial suggestions that most people would often consider for a horse team because he provides some def (whereas the rest of the team tends to have poor def except Reinhardt who gets doubled by everything and probably dies anyways) and because he can spam specials endlessly, great with vantage, even uses DC well, etc. etc.

Frederick is also very good, actually, if you ask me. Someone on my friends' list is merging one with a brave axe, death blow, QR, close def, and ignis. I've even taken out some reds with this unit and tanked some reds without strong player phase. That said, for cavalry tanks I don't know of any I prefer over Sigurd. He'll tank anything except dragons, including Reinhardt.

Raven+TA+bowbreaker Cecilia is great at countering Reinhardt and B.Lyn, which is kind of ironic because a lot of people use her as a green mage in a horse team so it's using a horse to counter horses, but it's a perfectly reasonable option. My personal preferences for greens on a horse team are WT Olwen (blade tome without cooldown penalty) and G.Marth; I use Cecilia as a counterpick when I'm playing arena assault because she's slow, and Gunnthra (who a lot of people play with a blade tome; decent choice but not my taste) I prefer in a mixed team involving a dagger unless she has a cavalry healer running a bunch of ploys or using dazzling fear+ res smoke and spd smoke. (Elise would be great for this, actually, if there's a spare Genny to give her wrathful staff; she gets pretty fast and can do a lot of damage.)

Were you looking to build a melee-focused horse team? It's not the common route, but it's by no means wrong.