(I haven't tried this so my apologies if it doesn't work)
Google Now appears to have support for Microsoft Windows and is supported by 52 languages (one of them being Korean). I believe you can download its equivalent on Microsoft Windows via the Microsoft Store and have it as an app on your PC (the Google app, there are 2 but the other doesn't appear to have support for Windows), given that you're running 8.1 or greater. I'm not aware of all of its capabilities as I haven't tried it, but maybe this can act as at least a partial solution.
Under 'Supported Languages' on the linked webpage is "한국어(대한민국)". The app lists its capabilities as "Use your location, Use your microphone, Access your Internet connection". More specifically on the voice dictation, under 'Features' the app says it has "Voice Search - Use your microphone to ask Google anything and see the answer instantly."
EDIT: If this doesn't work, then after extensive search I would vouch that at the moment there isn't any program on Windows capable of doing what you want.