It does not appear there was a Cavalry component assigned Thomas' Legion.

Vernon Crow's "Storm in the Mountain"s lists a 10th Seiber,

Anderson Seiber, 18, Private, Company K, Infantry Regiment, Thomas’ Legion, enlisted February 6, 1863 at Winter’s Gap by Capt. T. A. Butler for the war, receipted for an issue of clothing September 27, 1864, no further records

Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of North Carolina