The intertwined "SW" was trademarked by S&W on January 19, 1892. Their Declaration Statement for the application states the trademark has been "used continuously in business by us since January 29, 1878....It has been our practice to fix our trademark on our firearms by engraving or stamping the same thereon, to employ it in our illustrated catalogue of revolvers made by us, upon our different commercial papers, and to stencil or print it upon boxes or packages containing said revolvers."
Based upon the above, my guess would be the logo first appeared on their firearms after January 29, 1878 and before January 19, 1892.
John Gross