Against the CPU the Hippus can use mounted units much like any civ uses anything else until Tier 4 units are on the scene, where mithril champions and Arquebusiers obsolete them. (But mithril mounted mercenaries remain pretty cool)
In general Mounted units have a few specific niches. Horsemen are hilarious if you can deny metal to your opponent. Organise your Horsemen into triplets with a mix of promotions and strip pillage an opponent then sit on hills and chase any worker who tries to leave a city. Their economy will never recover. Unfortunately they'll just feed XP to bronze Axemen.
Horse Archers arrive on a cheap technology and will enjoy a brief season of battlefield supremacy which should be used to harass enemy Settlers and outlying settlements while still being able to return to your territory in time should a big stack show up. But without use of the Bless spell or acquiring of Nightmares from Hell terrain they will be a dead end and require building a whole new army for the next stage of the game. Even the slight strength upgrade will just delay their demise.
Chariots are a cheeky option that give flexibility for someone going a melee/siege route. Their poor defense means they get flattened by melee (or even Rangers!) when unsupported. If you move them with a stack they can suck up improvements as you move across them and threaten any vulnerable unit at reasonably long distance.
Rhoanna is an incrediby vanilla civ who should probably use mostly melee units supported by high movement mounted units. Expansive/Financial means she is incredibly frontloaded and should have a very high score and economy in the early game. It should be reasonably easily achievable to found Ashen Veil. A midgame army might be something like Champions/Ritualists/buff Adepts/Nightmare Mounted units. The mounted would move with the stack and force opponents to split their defenders between cities, because any city within 5 tiles that thinks it can donate most of its defenders to another city will get flattened.
Tasunke is something else and is the Hippus as most people think of them. With him I'd put all my eggs in one very small basket. Scout your opponents early, pick the weakest one and roll over him using Warcry. Perhaps you should even create a weakest opponent by using a small warrior stack to sit on their copper. You'd want to maximise in this order: Unit survival, XP gained, turn advantage, gold pillage. Its unimportant whether you finish this opponent off, just that you generate veterans, pay off the costs of your army, maybe advance your research a little and possibly create a punching bag for later. If you've been very quick you may be able to use your veteran horsemen lead by those who still have Warcry to hit another opponent. This second opponent may have metal and would have been untouchable without all the 10+xp units you should now have.
While you've got good units and other people's gold you can't afford to waste them. Turn those Horsemen into Horse Archers and hit the strongest opponent. Same mission parameters: Don't suicide into his strongholds, keep building up your XP in your units by running past the strong cities and razing the outlying ones. You don't have to kill him, you just have to ruin his economy and slowly bleed away his army in repeated small opportunistic attacks. If something scary appears then run away using the opponent's own roads.
The Order is probably a good fit for a religion. Bless new Horse Archers and they'll be very successful at farming XP in whatever punching bags you've left alive to this point.
At this point you should decide on the course of the rest of the game. Your mounted units are strong enough to attack even the best defended cities with reasonable odds and Iron isn't quite on the scene yet. You can either: 1) Pick the one or two opponents whos lands neighbour yours and add their cities to yours. You will probably take heavy casualties but thats ok because it allows you to transition into an Iron Champion army. You settle down somewhat with a large empire, an economy 20 turns behind where a builder game would be and the opponent's 50 turns behind you. 2) Contemplate the complete destruction of your enemies by getting Iron working, Guild of the Nine, adopting Consumption and Mercantilism where possible and turning your economy to 100% gold, Emphasise hammers, hire Iron Mounted Mercenaries at all cities every turn and try to kill everyone all at once. If hiring a Mercenary costs 80 gold then he only has to pillage 2 Towns to make his money back. So, if he survives 2 turns and pillages 2 Towns/Villages/Hamlets then he has probably hired 3 Mercs. This can very reasonably snowball into small stacks everywhere pillaging then all suddenly converging whatever weakspots show themselves. If you want to keep cities then maybe research Fanaticism first and use Acolytes to generate free Crusaders for city defense.
Raiders makes the difference between Tasunke and Rhoanna. Mounted units are fragile and will die if you don't take care of them. When they are Raiders and you use them intelligently then they can never be caught. You will be required to gain vision into as many tiles as possible each turn, spot the opportunities, take them and then retreat to safety. Rhoanna's 4 movement Mounted can't do this reliably but Tasunke's 8 movement Mounted can.
Now contrast this with the Doviello where you just walk up to people and punch them in the face AND still enjoy the same level of success then you get the feeling that melee emphasis armies don't have to work so hard...