By the way, the official translation of the board game («Игра престолов») uses «Зима близко» (the winter is near), not «Зима приближается» (winter is coming). I've never read the books or watched the TV series, so I don't know which version they use.
A question about English: I have noticed that the definite article is rarely if at all used with the names of the seasons: winter, spring, summer, autumn/fall. Are they never used at all? So, you cannot say ‘The Winter is coming!’?
Простите, пожалуйста, что я прошу вопрос по английскому в русском курсе!
I speak British English natively and sentences both with or without an article sound natural to me (in most cases). Without one the sentence maybe sounds slightly more proper/formal/archaic/poetic. Some examples:
During (the) summer I wear shorts. In (the) winter it gets quite cold. After (the) autumn our garden looked great. Each year the ice melts before (the) spring.
I would usually omit the definite article if it is at the beginning of the sentence unless referring to a season during a specific year/length of time. *The summer has arrived The summer had arrived by then The winters were cold in our cottage
I speak American English natively, and including the definite article in your sentence-initial examples seems preferable but not mandatory--omission just seems a slight bit awkward. In a sentence-final adverbial it seems much better to include it, but not quite required--with omission more awkward to my ear.
I'm therefore finding DL's translations without any articles consistently awkward.
A quick explanation why the seasons don't use articles. They're treated somewhat like proper names. It is unusual to put an article in front of something unique. So... "David is speaking", "red is a pretty colour", "Russian is a slavic language" and "Winter is coming". You would use an article if they are being used like adjectives, "The David from accounting...", "the red dress", "the russian language" and "the winter coat".