The 1903 (straight stock, A-nothing) was made by Remington in June of 1942. Don't know about its history in WW2, haven't looked into it. The barrel stamp on the M1 is 1946, and the trigger guard includes the slot for the paddle trigger mechanism that lets you fire it while wearing mittens. It
might have seen use in Korea, but if the stock wear is anything to go by, it was likely just carried in garrison for formations and the like (one part of the buttstock is worn where it would rub against the belt/trousers, and not much else).
My M1A is currently in a Vietnam era, genuine M14 fiberglass stock. I of course have the red walnut stock in the closet that I could toss on it for a special occasion.