Here is a reply from the Cody, Wyoming gun Museum.
Hi Randy;
It appears to be a Winchester Model 1886 rifle. The serial number would be on the lower tang between the end of the finger lever and the screw hole at the end of the lower tang. If it is a later version, the serial number was stamped deeper and in block numbers. It may be readable after a little clean-up.
The Winchester Model 1886 Lever Action Repeating Rifle was manufactured from 1886 until 1935, with a total of 159,994 produced. Winchester developed this model for the use of the more powerful centerfire cartridges that were being produced at the time. The Model 1886 was produced in 10 different chamberings: .45-70 U. S. Government, .45-90 W.C.F., .40-82 W.C.F. (in 1886); .40-65 W.C.F., .38-56 W.C.F., .50-110 Express (in 1887); .40-70 W.C.F., .38-70 W.C.F. (in 1894); .50-110-450 (in 1895); and .33 W.C.F. (in 1903). The most popular caliber was the .45-70 Gov't.
The Model 1886 was the first repeating rifle of John M. and Matthew S. Browning design to be adopted by Winchester. That design, and subsequent modifications by William Mason of Winchester, made it a vast improvement over the Model 1876. There were several variations: sporting rifle, fancy sporting rifle, takedown rifle, extra lightweight takedown rifle, extra lightweight rifle, carbine and musket.
The Model 1886 had a walnut stock, case hardened frame, and blued barrel and magazine tube. Winchester discontinued the case hardened frame on all of their rifles in 1901 and used blued frames instead. Factory options were available at extra cost. Standard barrel lengths were; rifles 26 inches, carbines 22 inches, and muskets 30 inches. Extra lightweight rifles in .45-70 were standard with a round rapid taper 22 inch barrel. Rifles in 33 W.C.F. were standard with a rapid taper, round barrel, 24 inches long.
The early Model 1886's had the serial number stamped lightly into the lower tang. These serial numbers had a tendency to wear off if the gun was well used. Around serial number 120,000 the numbers were stamped deeper into the lower tang and the wear on the tang was not such an issue. The Model 1886 had a detachable lower tang and if the gun was returned to the factory for repair and the lower tang was replaced, the replacement tangs did not have a serial number on them. As a result, it is possible to have a Model 1886 with no serial number.