In these instances, the capitalization is valid as part of a title. However, the error occurs when the writer extrapolates this rule back into general prose. Seeing a sign for a "Summer Sale" does not imply that one should write "The bees are buzzing in " in a casual email.
In poetry and classical literature, seasons are often capitalized to reflect their status as mythological figures or powerful entities. In this context, the capitalization is grammatically sound because the word ceases to be a common noun and becomes a proper name—like Zeus or Aphrodite.
In standard American and British English, the seasons are common nouns. Therefore, they are capitalized only at the beginning of a sentence or when they are part of a proper noun phrase.
The most obvious exception is when the word begins a sentence. Like any other word in the English language, summer must be capitalized if it is the first word. Summer is my favorite time of year. Exception 2: Proper Nouns and Titles
This is most frequently observed in the naming of academic terms:
In standard English, seasons are treated as common nouns rather than proper nouns. This means that in the vast majority of your writing, summer should remain lowercase. Whether you are describing a vacation, the weather, or a specific year, the rule remains the same. For example: We are going to the beach this summer. The summer of 2023 was the hottest on record. I love the smell of rain in the summer.
AP Style: Always lowercase seasons unless they are part of a proper name.