To herald the winter, well, it just doesn't sound complete to me. The winter comes where? You might get away with "Winter this way comes" or "Here comes the winter." On the other hand "Winter has come" is fine because it's then obvious, and "Winter is coming" because it's still in flux. Whereas 来る, 오다, jön, those are complete statements in themselves.
Looks like English contractions are not popular, thus not accepted. My translation, "Winter's coming." was considered wrong, but when attempting to report it I found the new software has deleted the option, "My answer should be accepted" and no substitute is offered. Contractions are very commonly used in English and form a big part of everyday speech.
Duolingo automatically accepts pronoun contractions like "it's" or "I've", and negations, "don't" or "can't". I don't think the programming is in place for anything more, so those extra contractions would need to be accepted as separate translations.
Generally I recommend not using contractions with this programme, since, after all, it's just a computer trying to interpret your writing. And even almighty Google still struggles with this.
There's another argument against writing "winter's coming", though. It might be interpreted as a genitive, and "the coming of winter", which would have a different translation in Hungarian.
Also it's not idiomatic. :D
EDIT: forgot about this. If you're on the web version of Duo, the "My answer should be accepted" option is still available if you hit "Report a problem". It's now just the last item on the list.
Many thanks, RyagonIV, for your patient and comprehensive explanation. I shall curb my instinctive use of contractions which, in everyday speech may be perfectly understood by fellow native speakers, and thus considered idiomatic. However, in a language course of this nature, keeping in mind and adapting to your audience (albeit a computer) is simply good practice.
To interpret "Winter's coming." as possessive case (genitive) had not occurred to me (nor would it, had you not suggested same) but doing so certainly illustrates an entirely different perspective from that which was intended.
On the technological issue when reporting - yes, I am accessing Duolingo via PC. It is perhaps just as well I was unable to report, as it would only have "thrown a spanner into the works", given the potential for misinterpretation.
Thanks again for your insight, RyagonIV, your linguistic knowledge and skill will continue to inspire not only me, but Duolingo students everywhere.