The only way you can get the year (AND month) is to check the date codes, explained here:
They have date code stamps on the barrel which can be looked up on the manufacture date link on the Remington Society of America.
Check the date code stamped on the barrel, details on the Remington Society of America manufactured date link.
See related links for date code stamps
It's date code stamped on the barrel see related links for information on the Remington Society of America.
I checked www.oldguns.net and they show the manufacture date of Remington 1903A3 serial no. 3851292 as 1942.
RW isn't part of the serial no, it stands for Remington Works 1915
That is not a serial no of a Remington 1911A1 they stopped in 1945 with 2465139.