I do not know what a snapchat cartoon looks like, so at a disadvantage there 
(or not as the case may be ) (edit #2) Just had a search for snapchat cartoon, I do not think you will get this with Gimp. It might be possible but it is an extreme effect.
Gimp has a basic cartoon filter Filters -> Artistic -> Cartoon
Recently a good alternative to that came up, 'bede 2.10.py' A long thread about it here: http://gimpchat.com/viewtopic.php?f=11&t=19335 Also a good place to start a new thread and ask about making cartoon strips. More artistic people there than here.
Easiest place to download bede 2.10 is https://www.gimpscripts.net/ , scroll down a bit until you find it. It does rely on another plugin gmic_gimp_qt , a big plugin but worth it, get the Windows installer from http://www.gmic.eu
Edit #1: my try:
The original (left) and the bede plugin applied (right) Recently been looking at half-toning and the gmic_gimp_qt has a half-decent filter (botton right) and an old plugin the produces a desaturated image, which you could colorize, depends how keen you are.
(or not as the case may be ) (edit #2) Just had a search for snapchat cartoon, I do not think you will get this with Gimp. It might be possible but it is an extreme effect.Gimp has a basic cartoon filter Filters -> Artistic -> Cartoon
Recently a good alternative to that came up, 'bede 2.10.py' A long thread about it here: http://gimpchat.com/viewtopic.php?f=11&t=19335 Also a good place to start a new thread and ask about making cartoon strips. More artistic people there than here.
Easiest place to download bede 2.10 is https://www.gimpscripts.net/ , scroll down a bit until you find it. It does rely on another plugin gmic_gimp_qt , a big plugin but worth it, get the Windows installer from http://www.gmic.eu
Edit #1: my try:
The original (left) and the bede plugin applied (right) Recently been looking at half-toning and the gmic_gimp_qt has a half-decent filter (botton right) and an old plugin the produces a desaturated image, which you could colorize, depends how keen you are.