Stop mowing. Not right to mow and charge the customer when the season is over.
However what you can offer your customers is a weekly fall clean up.
Put a bag on yout mower, vac trac, lawn vac, and clean up the lawn and beds each week. Say Oct 26 is last week of mowing you then spend the next 6 weeks doing a clean up till Nov 30.
Say a customer's fall cleanup is $300. You charge them $50 a week for the 6 weeks. Keeps the cash flow coming in and makes the clean up job easier.