I have one just like it although the grips are plain with only a Colt emblem stamp at the top of the grip panels. Mine was manufactured between 1910-1926. It is perhaps my favorite handgun. Accurate little cuss.
There is another grip that is pretty common, the brown one with the colt medallion. I've seen 1903's with those around, but I don't know exactly when specific grip types were fitted.
Well, I haven't posted the Remington Model 51 yet, it's a very nice shooting gun. It points very naturally, and deserves the reputation for shootability that it has. OTOH, there's nothing wrong with the Colt, it's also a nice shooting little gun.