You should not capitalize the word winter since it is a common noun and not a proper noun. But there are obviously a few exceptions where one has to capitalize the word winter.
When winter is used as a title or when it is used at the beginning of a sentence (such as “Winter is Coming”) are two examples of when winter should be capitalized. Also when winter is used as a proper noun it should be capitalized. Winter can also be capitalized it when it is personified such as in a poem.
The word winter does not necessarily need to be capitalized considering it is a generic noun. People normally confuse this word for a proper noun and capitalize it based on it being a proper noun. Generally, the word winter should not be capitalized.
The temperatures are usually low during the winter season.
The Word Winter as a Title
When the word winter is used like a title one will have to capitalize it since it is a rule to capitalize titles.
The Winter Holiday Was Very Chilly
“Winter” was included in a title and we must follow title capitalization rules and capitalize it.
The Words Winter as a Proper Noun
It is a rule in the English language that proper nouns have to be capitalized, so when using the word winter as a proper noun you have to capitalize it.
The Winter Gala is an event held every year in December.
In this case “Winter Gala” is the name of an event so “winter” is part of a proper noun. Therefore it should be capitalized.