With horses you must bear in mind, untrained to war, they are very unpredictable if someone starts shooting around them. In fact, they are very unpredictable with someone walking by in a rain poncho or with a flag. Horses shy away from almost anything they have not been exactly trained to tolerate - I've seen an actor take a rather nasty tumble, when he fired a musket pistol while sitting on a horse, who had not been accustomized in loud noises.
So, yes, mounted infantry in the old Dragoon-style would be more likely than actual Cavalry style, fighting from horseback. Of course, you might be able to muster some horses from history re-enactors, who might have theirs trained for jousting and have a platoon of lancers. 
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"Listen to me, nugget, and listen good. Don't go poppin' your head out like that, unless you want it shot off. And if you do get it shot off, make sure you're dead, because if you ain't, guess who's gotta drag your sorry ass off the field? Were short on everything, so the only painkiller I have comes in 9mm doses. Now get the hell out of my foxhole!" - an unknown medic somewhere, 2013.
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