Was Cold Harbor the bloodiest battle in the Civil War?
No. Most historians agree that the Battle of Antietam (also
known as the Battle of Sharpsburg, fought on September 17, 1862,
near Sharpsburg and Antietam Creek, Maryland, was the
bloodiest single-day battle in American history, with
almost 23,000 casualties on both sides.
But it depends to some extent on how you define "battle." Cold Harbor was an engagement that lasted 13 days. The National Park Service considers that there were as many as 13,000 Union casualties (killed, wounded and missing) as against 2,500 Confederate. By this count, Cold Harbor doesn't even make the top 10 battles of the Civil War in terms of casualties, but it almost cost Grant his command and Lincoln reelection because of the lopsided casualty figures. What saved Lincoln was Sherman's taking of Atlanta in September.
The Battle of Gettysburg lasted three days, July 1-3, 1863, and cost more than 51,000 casualties on both sides, making it the bloodiest battle of the entire war, but it wasn't a single day battle.