I never really end my shooting season as I shoot targets all year around. Although, when I am done, I clean the barrel in the standard manner, run a light coat of gun oil inside the barrel, and wipe the outside off with gun oil also. I then store it muzzle end down. I have done this for over 20 years and so far it has worked fine for me, so I am not changing....

Shoot well, and be safe.. Happy New Year