Thomas Nast, Frank Leslie's illistrated news.
Edit - I will give credit for this answer. Nast worked for Frank Leslie's Illustrated Newspaper immediately before he started work for Harper's Weekly, and he didn't start work at Harper's until the summer of 1862, so presumably he was still working for Frank Leslie's during the early part of that year.
Although everyone who answered Harper's Weekly will be given credit for a correct answer, Frank Leslie's may actually be a better answer, since the question asked for the name of the newspaper for which Nast worked, and Harper's Weekly, technically, was a magazine.
Hoosier