Alice's Adventures in Wonderland focuses on Alice wandering around trying to get into a beautiful garden and having wacky adventures along the way, so there isn't really a villain for most of the book. The closest we come to a villain is the Queen of Hearts, who shows up once Alice reaches the garden. The Queen is a tyrant who has one solution for every problem – beheading! Her bloodthirstiness and her instant dislike of Alice seem dangerous for our heroine until we realize that, after all, the Queen of Hearts is literally just a playing card.
Despite the fact that Through the Looking-Glass is structured around a chess game, there isn't really an antagonist for Alice to struggle against. You'd think that the Red Queen, the most powerful piece on the opposing side of the game, would be the antagonist. However, the Red Queen actually assigns Alice her role in the game and gives her advice on how to succeed. When Alice makes it to the eighth square and becomes a Queen in her own right, the Red and White Queens are both there to celebrate with her. The conflict between the red and white pieces is only a structure, not a bitter battle, and the Red Queen is more of a guide and mentor than an antagonist.