The RNWMP began purchasing Colt New service revolvers in September of 1904, in .455 until 1914. From 1919 until 1942, all Colt New Service revolvers purchased by the force were in .45 Colt. ALso, after WWI the Webley Mk VI was an "ancillary" issue, used in small numbers until 1950
After 1914, the primary long arm would have been the Lee-Enfield carbine, but after WWI, the Mk III SMLE was much more prevalent.
There was a vast array of other firearms used by the Force. You would have to consult the Phillips & Klancher book, Arms & Accoutrements of the Mounted Police, 1873-1973.
P.S: There were some unusual ones, varying from the Savage 99 to the Maxim or Lewis