Well, I know virtually nothing about fly fishing but the fishing doesn't stop- just the season. The lower lake fishing season ends the end of the month but there ARE some lakes open year-round. Just look through the regs and they'll show you. There may be some Alpine lakes open all year but I don't know. You might try going to the Dept. of Fish and Game- http://wdfw.wa.gov
you might find more information there. Another site that might be helpful is: http://www.washingtonlakes.com
Where are you located? I know of three lower lakes that are open all year- Kitsap and Long Lake in Kitsap Co. and American Lake near Tacoma.
Hope this helps you and good luck!