Seasons Aren't Proper Nouns
In most cases, no. The names of the seasons—spring, summer, fall or autumn, and winter—are not proper nouns, so they only get capitalized when other common nouns get capitalized.
Why is summer not capitalized?
Seasons, such as winter, spring, summer and fall, do not require capitalization because they are generic common nouns. ... However, the four seasons are not proper nouns and, consequently, do not need to be capitalized.
When should you capitalize summer?
If you use summer as a proper noun, such as in “Summer Semester,” it must also be capitalized. Another exception in which you should capitalize summer is when it is personified in poetry. Apart from these exceptions, there is no need to capitalize seasons, including summer, for any writing purposes.