Is season a proper noun

No, the noun 'season' is a common noun, a general Word for any of the four divisions of the year (spring, summer, autumn, and winter).

A proper noun is the name of a specific person, place, or thing; for example:

• Season Hubley, American actress
• Season Drive, Milton, FL
• Spa Season, New York, NY
• "A Season in Purgatory" a novel by Dominick Dunne