Try these steps:
1. Create a calculated field to tag which season the date belongs to
2. Bring sales to view and use table calculation to get the desired result
Calculation Type: Running Total
Compute Using > Specific Dimensions> "Season" and "Day of Order Date"
Restarting every "Season"
Attached file using sample superstore data for the reference. Please close the thread if it helps you and solves your problem.
Season2Date_10.4.twbx 1.2 MB