Maybe the 1920’s?
After WW1 ended, Winchester needed to diversify, in order to survive as a company; and merged with the Simmons hardware stores (that already sold their firearms). About that time, E.C. Simmons likely sold Snyder built bicycles, (after Miami?).
By the crash of 1929, the 2 companies had parted ways.
The junior roadster example for auction looks like a Westfield built bicycle, based on the chain ring sprocket. The earliest ad for a junior roadster (drop bar or camel back) that I recall was about 1920.