William H. Wheeler was born around 1835. By the early 1860s, he was living in Adrian, Michigan. He enlisted in the Union army on August 21, 1861, and he mustered in as a corporal in Company E of the 1st Michigan Cavalry on September 4. The regiment took part in the Battle of Cedar Mountain, the Second Battle of Bull Run, the Battle of Gettysburg, and the Overland Campaign. Wheeler was promoted to 1st lieutenant on November 12, 1862, and he mustered out on October 22, 1864. He applied for a federal pension in August 1892 and eventually secured one. He died sometime after 1892.