One thing I see missing in your source code is the DOCTYPE I have:
above the html tag. The doctype gives information about the document to the browser, though I don't know how much it would affect the charset when it's missing.
That's the only other hint that I can give you other than that I can't see anything wrong from here.
I don't think that a plugin would solve this, this is a WordPress related issue, some type of setting is switching the charset to something else (probably the default limited ISO charset).
I have a WordPress theme on my local server with only the default plugins installed and no additional plugins, and I've just tried posting a Korean text and it showed up without any problems.
Since you said you have imported the content to your hosting server, I'm guessing you must have imported it into a MySQL database right? In that sense this can also be a database related issue.
Please look into your MySQL database in your wordpress table and make sure that your collation is set to
utf8_general_ci if you have set it to something else it will - as well - not work.
p.s. Don't forget to post a new post in your blog once you have switched the database setting.