[jabomano]

This photo is from 1914 and colorized digitally. Does anyone know what gun this is?

 

[bearcatter]

Welcome aboard!
Best I can tell from matching photos, it's a Winchester Model 1886. Manufactured 1886-1935, made in over a half dozen calibers. The only change it needed when smokeless powder came in was a stronger nickel-steel barrel (apparently 1903). I hope this helps.
More detailed history on Wikipedia:

Winchester Model 1886 - Wikipedia