Any kind of art school, particularly those with degrees in illustration and sequential art, will help you develop your artistic skills. Illustration for evoking mood, and cultivating general technical skill. Sequential for teaching you movement, pacing, camera placement, and so on.
That said...
I don't know where you're located, but unless you live somewhere with free university education, an art degree is expensive. It's not something I'd recommend without putting some serious thought toward your current financial situation, and your ability to pay off future debt. Plus, from the stories I've heard, the more prestigious art schools can be demoralising burnout factories.
There's a lot you can pick up just by studying online courses, following tutorials, and just drawing every day in general.
I'm not a trained artist. I've just been dabbling for years. I only decided to make a proper go of a visual art career a year ago. (I got bored with teaching music full-time. 
) The quality of education, advice, and insight into the artistic process of professional artists you can find online these days is mind-bending. Avail yourself of it. Be a sponge.
Oh, and it's easy to forget, but being able to draw is only one half of making a popular webcomic. You have to be a compelling writer. So start reading. Novels, comics, short stories. Screenplays. Movie scripts. Join a writer's group.
As for becoming employed as a comic or webtoon artist, there are a few paths you can pursue.
1. Self Publishing: Create your own comic, build an audience, and make your living through Tapas/Webtoon ad revenue, Patreon/Ko-fi, merchandise sales, private commissions and so-forth. This is what many creators on WEBTOON and Tapas are doing, with varying degrees of success. Regardless of whether you make it 'big' doing this, it can be a good place to practice and refine your skills before launching toward one of the paths below.
2. Traditional Publishing: There are two rather distinct 'universes' in traditionally published comics right now, with each appealing to different creators working in different styles. One is working for the old-school comic book publishers like DC and Marvel. They often still break up the artistic process into pencillers, inkers and colourists, so if you cultivate a high degree of skill in any one of these, this can be a solid option. That said, these comic houses have begun struggling to maintain profitable book sales, and are being kept alive by their film licensing. If you follow this road, make sure not to let the skills you're not working with daily languish. You may need 'em.
The other is working with book publishers, as an illustrator of middle-grade and YA graphic novels. These include Penguin Books, Scholastic, Harper Collins and so-on. Totally different universe. You're technically working more like an illustrator in this world. They look for illustrators who can solo a whole book, so if you don't want to be pigeonholed into just colouring, or just sketching, they're a good option. They also gravitate toward a more diverse range of stories and genres, rather than just 'superheroes'.
Plus, unlike the old-school comic houses, this is a market which is exploding with growth due to the education market finally realising that graphic novels are a gateway drug to literacy for many a reluctant reader.
3. Online In-house Publishing: Something I was very excited to learn recently is that Tapas actually hire artists to be part of their in-house publishing team. It's far too early to say if this will remain a viable option long-term, but it's there at the moment. WEBTOON probably do this too, but I expect they're more likely to hire Korean artists since that's where they're based.
