That he did, and to this day Lincoln's shawl is in public view along with a collection of other Lincoln artifacts in the Lincoln museum at Ford's Theatre. It is an extremely effeminate shawl at that and has volumous and lengthy frills extending from its edges at least 4 inches. It is a beige color and would not be out of place decorating an old lady's couch or wrapped around her head in the coldest days of winter...just as Lincoln did on his way to the inauguration!
Mr. Lincoln and Colonel Lamon got on board the car without discovery or mishap. Besides themselves, there was no one in or about the car but Mr. Lewis, General Superintendent of the Pennsylvania Central Railroad, and Mr. Franciscus, superintendent of the division over which they were about to pass. As Mr. Lincoln's dress on this occasion has been much discussed, it may be as well to state that he wore a soft, light felt hat, drawn down over his face when it seemed necessary or convenient, and a shawl thrown over his shoulders, and pulled up to assist in disguising his features when passing to and from the carriage.
Ward H. Lamon, The life of Abraham Lincoln; from his birth to his inauguration as president, Boston: James R. Osgood & Co (1872), p. 523.