I believe the mobility and the lighter field pieces available made it impractical to form a square as they would only be a massed target for the artillery. I think the French army first started making lighter field pieces to accompany the cavalry to combat the square tactic.
The 4 and 6 pounders were always available. The differance was what the call foot and horse artillery. Foot artillery the gunners , well were on foot and walked or jogged along side the limber teams.
Horse artillery all the gunners were mounted.These were attatched to Cavalry divisions, maybe down to the Brigade level.Much faster to move and go into battry.
Forcing infantry into square with the threat of cavalry and then hammering the square with fire from the quicly deployed horse battery was a great tactic.
ACW Cav against infantry charges.Very few.I recall one at Chancelorville, Union cav slamming into Rebs blocking a road intersection, leaders all killed but they did break up the infantry formations, for a while.I believe in the same area where Jackson was shot later that evening.Troops thought he and his staff were Yankees cavalry.
Another in the Peninsula, cant recall where exactly but the Yanks were defending a hill, arty to the front, rebs got close and picking off gunners, cav charged thru the guns to brush away the infantry, rebs poured volly into them, cav retreated { with infantry right on their heels, hooves} back thru the arty .The gunners couldnt fire for hitting the cav and the retreat caused so much havoc the frightened arty limber teams retreated with the cav and the whole place folded into a paniced route.