겨울 is a noun, whereas 동계 is an adjective. 겨울이 온다 - Winter is coming, 동계올림픽이 내일시작해 - The Winter Olympics starts tomorrow.
冬季(동계) is technically a nominal, but the Sinitic forms are generally used in compound words and extended terms so in that way they act like English adjectives tend to.
Having never learned the English spelling of Korean cities, these are tough.
That's where romanization actually helps me instead of hinders me when I'm learning. For example, 평창. The way to spell it is Pyeongchang:
ㅍ=p, ㅕ=yeo, ㅇ=ng, ㅊ=ch, ㅏ=a, ㅇ=ng.
It's like that with many other Korean cities too:
Seoul: ㅅ=s, ㅓ=eo, ㅇ=(nothing... it's before a vowel), ㅜ=u, ㄹ=l.
Busan: ㅂ=b, ㅜ=u, ㅅ=s, ㅏ=a, ㄴ=n
Gwangju: ㄱ=g, ㅘ=wa, ㅇ=ng, ㅈ=j, ㅜ=u
Can someone tell me why "Pyeongchang Winter Olympic" wouldn't be accepted? I know it doesn't make much sense, but the 올림픽 doesn't have the "s" sound.
It's probably because English is weird, needing the 's' to make the adjective a noun and so final, and the modern Olympics started in France where it's actually Olympique?