I personally have no idea though it occurs to me that this might have been better asked in the Vintage Tool Discussion threads where i suspect there's more members who might know.
That said, I gave it a google and to my eyes the Snap-on 1920s logo looks similar to yours as opposed to the 1930s where the font is a little different and the dash is angled instead of straight like yours, BUT sometime after that (40s/50s?) the logo looks to have changed again and it also looks a lot like yours to my eyes so

. If I
had to guess I'd probably go with the latter.
[EDIT: Actually on a second take the dash actually is also angled in the 1920s similar to the 30s.
So it looks to me sometime around 1950-ish in the pages below the logo starts to look more like yours, so, there's that
]
Anywho, you might wade through these pages for a few clues to see if you see something differently than I. Might have better luck putting the images side by side to better compare than my flipping back and forth.
Snap-On: Early Sockets and Drive Tools (~1920s)
http://alloy-artifacts.org/so-early-sockets.html
Snap-on and Blue Point Tools, 1930-1959
http://alloy-artifacts.org/snapon-bluepoint-tools.html