Clay pipes definitely. Both white and terra cotta clay pipes have been excavated at both Union and Confederate campsites. During the Civil War, most clay stem clay pipes were typically shorter stems than their 18th c. counterparts. Clays were very fragile, so a shorter stem clay pipe was much easier to carry in the field with less risk of breakage. Reed stem clay pipes were also extremely popular, probably more so than their clay stem counterparts, as the pipe could be "dis-assembled" for easy transport on the march and then quickly reassembled when ready for use. Also, if the reed became damaged, it could easily be replaced by cutting another reed in the vicinity.
Corn cob pipes were also in use. During this period they would have been handmade as the commercial manufacture of cob pipes didn't occur until after the Civil War (credited to Henry Tibbe, founder of MM, around 1869). These "homemade" corn cob pipes would have had simple. but functional reed stems like the reed stem clay pipes.
Carved wood pipes were also in use, usually with hollowed wood stems such as walnut or cherry, and fitted with mouth bits, typically made from horn or vulcanized rubber, or carved from wood. Briar pipes were in existance but somewhat rare in North America in the 1860s. Wooden pipes are often seen being used by officers in period photographs, but many enlisted soldiers used them as well and often carved them themselves out of available wood around their campsites. Soldiers would have typically carried these in their knapsacks while on the march to protect them from damage until they were off duty and could put them to use.
Meeschaum pipes would have also been in existance during the War, but meerschaum pipes in the 19th century were very expensive and somewhat exotic, so it would have been somewhat rare to see an enlisted soldier smoking a meerschaum unless he took it off the body of a fallen enemy officer. When meerschaums were smoked, it would most likely have been smoked by higher ranking officers in both the Union and Confederate armies.
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