Lincoln was a legendary wrestler. Legendary because much of it is a part of the Lincoln mythology. Lincoln certainly wrestled in his days, but the truth probably has a politicians spin on it. Lincoln's reputation as a fighter and fair dealer were important to his image as a self made frontier politician. Many of the early biographies about Lincoln, especially those written shortly after his death have an almost formulaic section about Lincoln wrestling. Carl Sandberg's 1926 biography Abraham Lincoln: The Prairie Years recounts the story of a young Lincoln wrestling a town bully. The story is mythic in its structure. Lincoln is a reluctant fighter. He defends the town from the bully. The opponent cheats, but Lincoln still wins fairly. Lincoln befriends the bully even after defeating him. It is like the WWE staged the American Civil War.

All that said, Lincoln probably did wrestle as a young man. On August 21, 1858, at the first of the famous Lincoln-Douglas Debates, Douglas, who had known Lincoln since they were young men, remarked that "[Lincoln] could beat any of the boys wrestling, or running a foot-race, in pitching quoits or tossing a copper; could ruin more liquor than all the boys of the town together, and the dignity and impartiality with which he presided at a horse-race or fist-fight, excited the admiration and won the praise of everybody that was present and participated." As you can tell from the second half, he was much more famous for being a fair dealing referee than a wrestler.

William Hendron, his law partner in Springfield, described Lincoln as a large and strong man, and recounted several stories of seeing him lift between 1,000 and 1,300 pounds of rocks or defeating scattered opponents in wrestling matches. Lincoln grew up working hard his whole life, so it is certainly possible he was a very strong man. Long days working in the wilderness, and then spending his youth as a boat poleman, combined with his massive size certainly could have crafted an exceptionally strong man. I will add that the world deadlift record is only a hair over 1,000 pounds, so it seems likely Hendron saw Lincoln lift a lesser, but still impressive weight.

As to what kind of wrestling, Lincoln was never formally trained in anything like Greco-Roman wrestling. Most likely they were impromptu affairs designed to demonstrate who was strongest, quickest, or most cunning, while preventing any real injuries. Surviving folk wrestling games often start with the two opponents in a particular stance or grab and then attempt to topple the other. In some you cannot move your feet, or you can only shove the opponent and so on. Jacket wrestling is the most common type, where you can only grab the jacket or belt of the opponent and then use any means to throw them to the ground. The games were intended to be fun but physical, while sometimes training a real skill.