Not to discourage further answers, but I found several answers while searching:

This one by /u/Iago_Huws about the differences between cavalry in the Napoleonic wars and the American Civil War:
https://www.reddit.com/r/AskHistorians/comments/29qo2s/napoleonic_cavalry_uses_versus_american_civil_war/

This one by u/DuxBelisarius touches on why cavalry in the Civil War operated the way it did:
https://www.reddit.com/r/AskHistorians/comments/51hcib/why_did_cavalry_during_the_us_civil_war_operate/

Finally this one by u/Clockt0wer on cavalry traditions in the US:
https://www.reddit.com/r/AskHistorians/comments/6g2mfm/why_did_the_usa_never_develop_a_europeanstyle/