Particular seasons are temporal elements, in exactly the same way as a day of the week or a month of the year. They pinpoint a specific region of time. As such, seasons should be capitalized. However, the actual word 'season' (like any generic time period), should not be capitalized, as a particular time period is not being specified.
In many areas, school now starts in the middle of Summer, technically. --
We're planning a trip for sometime next season.
The next tournament isn't until November. --
There is an event planned every month.
Your car will be ready on Wednesday. --
Your order should get to you in a few days.