Cartoonists are visual artists, ones who work within or outside of the comics industry to plan, create, and publish illustrated cartoons in various genres. There are many forms in which a cartoonist could take their work in, such as storyboarding, comic strips, posters, advertisements, etc. Basically, a cartoonist is someone who either sells their freelance work to buyers interested in their continued works, or someone who is hired out by clients with a particular purpose in mind. The definition of cartoonist has considerably broadened over the years with the advent of digital medias, expanded definitions of art, and new ways with which people engage in art. You could work purely in pen and paper, paint out large cartoons and upload them to the internet, create a printing press of comics, etc etc.
In order to be a successful cartoonist, you need to be able to either create and cultivate a series of works which draws in an audience willing to buy what you make, or you need to have a wide enough skillset and distinctive enough art style to attract clients willing to pay you to make a certain illustration. Draftsmanship and craftsmanship is an essential skill in either path, but you also need to have good outreach to people who might be interested in your work.
While there aren't specific college programs for cartoonists, most illustration programs would work nicely in cultivating the necessary skillset. Northeastern Univ, Brigham Univ, and the Rhode Island School of Design all seem to have nice programs in this field.
