Sure, but the GoT quote is translated rather as "Nadchodzi zima", I can also imagine "Zima się zbliża", they have more... pathos ;)
But yours is perfectly fine, just pretty... neutral.
With this sentence, how do you tell the difference between 'the storm is coming' and 'the storm is going'?
If anything, then "The storm is going", as for Verbs of Motion it matters whether you use Present Simple or Present Continuous.
Either you posted that thr second I posted my response or I didn't look very hard. I am still having trouble with the sentance structure, I guess.
Of the Polish sentence? "Burza idzie." works as well. It's a matter of what is new information. If you expected a storm, then "Burza idzie." makes more sense. If you didn't, "Idzie burza." seems better.
It seems like "Burza idzie" is more likely to be translated as "The storm is coming", and "Idzie burza" is more likely to be "A storm is coming", right?
If I wanted to stretch the English language a bit, I'd say "There is coming a storm."