The Battle of Blackburn's Ford is an introduction to the Combat Command American Civil War Rules. The pdf also includes counters if you don't have figures.
Rules: American Civil War
Warhammer American Civil War Variant
The Cops.NU site has a Warhammer 40K variant for the American Civil War. I think it could work.
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Fire and Fury America’s Wars
I think Fire and Fury is the finest set of miniatures rules ever written. It has elegantly simple mechanics, fun gameplay and set the standard for high-quality rules presentation.
Now the Fire and Fury people are at work on a version for America's other "horse and musket" wars: The Revolution, War of 1812, and Mexican War. You can find the playtest versions of Fire and Fury: Americas Wars here.
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Tin Army In The Civil War
Tin Army In The Civil War is a set of free wargames rules for the American Civil War by Ross Mcfarlane. The author writes:
This is a simple set of wargame rules aimed at Division or Corps sized battles. They assume that low level tactics are being handled by regimental officers and their Brigadiers and by the dice. The game may be played on grid with 1 unit per grid area otherwise all distances are roughly equal to the frontage of a deployed infantry unit or roughly 150 yards. Units within that distance and directly in front of, behind or beside each other are deemed to be adjacent. Turns represent a variable length of time and overlap the previous and following enemy turns. 12 to 15 turns each is a good medium length game with a simple scenario and a dozen or so units per side.
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Most Irregular Horse and Musket Rules
Most Irregular is horse and musket rules extension to the Fast and Dirty skirmish rules, found on the same page.