The cartoons are socializing our children to reinforce the earlier patterns/ attitude o f societies over gender perception. As we perceive the world as male dominating society (critical/ feminist approach), we can assume that they cartoons are being made to follow the same path
I strongly agree that cartoons can certainly socialize our life, thinking , development of attitude. till now tom and jerry, pogo channels attract a huge crowd irrespective of gender, age , class and creed. so through cartoon we can certainly change the attitude of the people
I do not know of a study that deals with stationary cartoons (for example Charles Schultz's Charlie Brown) or animated cartoons (for example Tom and Jerry as was mentioned by Sunitha Gandhavalla Ganiger above).
Further, a great many people would become angry if I were to conflate animated cartoons with computer games, so, I must not do that. However, I would like to suggest that the work of Anita Sarkeesian in the domain of computer games in some ways appears to parallel your question. As far as I know, Sarkeesian's work is intended to serve the gaming community, which includes developers and players, and she has not published her research yet in any academic journal. (Please correct me if I am wrong and provide the references!) Perhaps she is keeping her data private until she publishes it in some number of articles or as one selection from a number of possible research problems for a dissertation.
From the anger and the praise her work has attracted, I think that there is little doubt that her question, like yours, is an important one. Until Sarkeesian publishes her work, perhaps one way to answer your question would be to search for themes and "Likes" and "Dislikes" (is there such a thing as a "dislike"?) in social media around her video reviews as a way to quantify the answer to her question, which would perhaps parallel the answer to yours.
Here is her web page. I believe that this has links to her YouTube channel
http://www.feministfrequency.com/
I was fortunate to hear her 2012 talk at TEDxWomen and meet her briefly afterwards. I recommend the talk as background information http://www.tedxwomen.org/
Check out Klein and Shiffman's 2009 paper "Underrepresentation and symbolic annihilation of socially disenfranchised groups ("out groups") in animated cartoons". The authors examined cartoons over a 60-year period. It appears that the representation of female and male characters has not changed much over the years (e.g., physical attractiveness was important for females, whereas intelligence was important for males). Arguably, cartoons are still perpetuating gender stereotypes. It's an interesting read.
The cartoons are considered a Mass Media, and the Mass Media it´s a socializing agent. When the kid see the cartoons it´s in the most time in the secundary socializing. In this fase, the children learn the gender roles throught three things: family, friends/school friends and the mass media. On the on hand,The cartoon represent to the kids the "normal things", so when appear a stereotypical girl, they thinks that´s it´s the normativity.
On the other hand, when it appears empowered girl, they learn other "normativity".