There seem to be two words for each season. Each pair has the first character in common but for the second character one will have 季 (jì) and the other will have 冬天 (tiān).
For example "winter" is:
What is the difference between the two? I can see the first uses the character for "season" and the second uses the character for "heaven", but this doesn't seem to tell me anything useful.
冬季 is more formal than 冬天. When used to refer to the season itself, the former is more commonly found in literature, the latter in vernacular.
However, when used to refer to something of that season, i.e. in a noun phrase, the 冬季 form is almost always used. For examples, "winter fashion" is 冬季服装, "Winter Olympics" is 冬季奥运会*. You would never use 冬天 for these, unless rephrasing them in a very informal way e.g. 冬天穿的衣服.
*: if they don't get abbreviated awaylike 冬装 or 冬奥, that is.
冬季, more like talking about the season it self, for example "冬季是睡觉的好季节。", "今年冬季假期有 2 个星期"
冬天, commonly used; refer to the time in Winter, such as "今年冬天，我将去北京旅游。"
Yes, 天 means heaven sometimes, but 天 can also mean weather. Most of times, they are both exchangeable.
冬天真冷-冬季真冷
相约在冬天-相约在冬季
今年冬天不下雪-今年冬季不下雪
Maybe a native Chinese speaker will find some of the sentences are kind of weird, but people will understand your phrases none less.
冬天 is much more commonly used in oral.
冬季 sounds very formal and you probably will only see it in a geographic science book or hear from National Geographic show.
Nothing wrong if you use 冬季 when you talk with people, but just sounds formal.
冬季 (and other season names containing 季) is a formal term, used mainly in writing (书面语). 冬天 is a frequently used term. In practice, I guess it should be OK if you recognise both, and use the latter.
季 = Season 冬 = Winter, Cool ...
