I recently picked up a Model of 1903 made at Rock Island Arsenal circa September 1918. It was likely manufactured too late to have made it into WWI. Perhaps used in WWII, as it was used hard enough to be refurbished late in the war at Raritan Arsenal. It came to me with Cosmoline left in a few places, including the bolt, chamber and magazine follower, so it's quite possible it was not used after refurbishment.
It's always fascinating to decipher the markings and learn as much of the story as possible with these old firearms. It was rebarrelled with a coveted High Standard barrel made in July 1944. My CMP gauge reads about 0.5 (certainly well less than 1) at the muzzle, which means it has a new to near new bore of less than .301 diameter. The bore is bright and shiny and an oiled patch came through with some dust and light brown Cosmoline residue. By the third patch it was clean. The barrel replacement was done during a complete rebuild at the Army Ordnance refurbishment facility, Raritan Arsenal (RA-P stock marking), where it was outfitted with a Remington (R) stock and mid-1941 Springfield Armory (BF 19 steel lot code) bolt. The serial number indicates this M1903 was made after introduction of the double heat treatment to ensure strong but not brittle receiver, and before the nickel steel receiver blanks were introduced. The upper barrel band is Remington (R) marked. To complete the picture, the lower barrel band is U marked, consistent with WWI production. The smooth buttplate is also WWI era production.
All of this means that it's a refurbished mixmaster that, with respect to shooting, should be in like new condition some 75 years after being refurbished. I love shooting my Springfield Armory 03-A3 and I'm looking forward to giving this Model 1903 a go at the range.
The ivy in the picture does not imply that it was used by the 4th Infantry Division, but you never know