best fighting horse units?

[athanaric]

Most of those would be factional. Basically, they are recruitable from "cultural" pools, i.e. depending on your faction's culture.

If you play a Successor kingdom (AS, Ptolies, Makedonia, Baktria):

Lance&Kopis (AP)
Hetairoi (morale 18 (!), armour 18, good stamina) are the best you can get (and one of the outstanding cavalry units in the game; probably the best all round).
Hellenikoi Kataphraktoi (morale 13, armour 22) are even heavier (better armour and charge), but suffer from lower morale and stamina.


Iranian and Hai kingdoms (Saka, Pahlava, Sauromatae, Hayasdan):

Lance&Longsword (high lethality)
Grivpanvar (Pahlava only; morale 16, armour 26 (!)) are the heaviest recruitable unit. Eats everything from HAs to legionaries.
Asavaran-î Âzâdân (Pahlava only; m 14, a 20) are decent enough.

Lance&Mace (AP)
Pahlavân-î Zrêhbârân (Pahlava only; m 16, a 20) are very useful, especially against other armoured units.
Ysaninu Aysiramjä (Saka; m 16, a 18) are my favourites.
Armenian Nobles (Hai only; m 18, a 18, good stamina) are one of teh best!


Others:

Lance&Falcata (AP)
Iberi Lanceari (m 15, a 16+2) are Southern Iberian regionals for Qart Hadast and Lusotannan. Very nifty.