Differences between the two words for each season, such as 冬季 (dōngjì) and 冬天 (dōngtiān)
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.