Doubtful that these would contain a roster, but the National Archives in RG 109 shows the following records for the Texas 1st Heavy Artillery Regiment available online:
https://catalog.archives.gov/search?q=texas%20heavy%20artillery&f.ancestorNaIds=438
Morning Reports, Col. J.J. Cook's Regiment, Texas Heavy Artillery, 1865
From RG: 109
Record Books of Executive, Legislative, and Judicial Offices of the Confederate Government
National Archives Identifier: 7557439 Local Identifier: Chapter VIII, Volume 111 HMS Entry Number(s): PI101 3
Creator: War Department. The Adjutant General's Office. War Records Office. 1874-7/1/1899
Morning Reports, Col. J.J. Cook's Regiment, Texas Heavy Artillery, 1864-1865
From RG: 109
Record Books of Executive, Legislative, and Judicial Offices of the Confederate Government
National Archives Identifier: 7682666 Local Identifier: Chapter VIII, Volume 112 HMS Entry Number(s): PI101 3
Creator: War Department. The Adjutant General's Office. War Records Office. 1874-7/1/1899
Morning Reports, Col. J.J. Cook's Regiment, Texas Heavy Artillery, 1864-1865
From RG: 109
Record Books of Executive, Legislative, and Judicial Offices of the Confederate Government
National Archives Identifier: 7682667 Local Identifier: Chapter VIII, Volume 113 HMS Entry Number(s): PI101 3
Creator: War Department. The Adjutant General's Office. War Records Office. 1874-7/1/1899
Military Departments -- General and Special Orders Issued and Received, Col. Joseph J. Cook's 1st Regiment of Texas Heavy Artillery, October 1861 - October 1862
From RG: 109
Record Books of Executive, Legislative, and Judicial Offices of the Confederate Government
National Archives Identifier: 28470885 Local Identifier: Chapter II, Volume 242 HMS Entry Number(s): PI101 3
Creator: War Department. The Adjutant General's Office. War Records Office. 1874-7/1/1899
Military Departments -- General and Special Orders Issued and Received, First Regiment Texas Heavy Artillery, May 1862 - July 1863
From RG: 109
Record Books of Executive, Legislative, and Judicial Offices of the Confederate Government
National Archives Identifier: 24622260 Local Identifier: Chapter II, Volume 243 HMS Entry Number(s): PI101 3
Creator: War Department. The Adjutant General's Office. War Records Office. 1874-7/1/1899