Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In responding to your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
You need to ask yourself these three questions to decide whether what you are doing is halal or haram:
1- What beneficial purpose does your work serve? Does it help society by promoting virtue or provide education that contributes to human welfare?
2- Is your intention pure and sincere to serve Allah and the community?
3- Is the content pure or free of all obscene message or suggestions?
You can satisfy these questions, and then there is no harm in using cartoons or drawing in Islam for the simple reason it is a medium of communication. As is the case with any other medium of communication, the criterion that makes it halal or haram is what purpose it serves; if it serves a useful purpose, it is considered permissible or even recommended.
One crucial point to consider in evaluating the use of media is that today it is used by those who seek to spread corruption on earth most efficiently; it is a weapon they wiled most efficiently. So, if we were to refrain from using it for a beneficial purpose, we help them win over.
Almighty Allah knows best.