The value of ANY gun is based on EXACT make, model, and condition. Smith ^ Wesson made several revolvers in caliber .32 Winchester (also called the .32-20) so we do not know model or condition. Value could range from $50 to several hundred. You would need to visit a local gun shop or gun show for a hands on assessment. You can also check through the Blue Book of Gun Values (library may be able to get a copy for you) and match up what you have to the book. Those were well made guns- in good condition, could have significant collector appeal.
@1969
1977
No serial number given = no answer.
1969
1979
You must call S&W
1986
80-81
You will have to call S&W
You must call S&W
You will have to call S&W for the date.
Call S&W with the serial number and they will tell you.