Using my collection and reference material, I have been able to narrow the missing logos down to no logo dates. I have 32 Winchester 47736 shipped March 1917 with large logo on right side. I have 32 Winchester 85057 shipped March 1920 with no logo.
As for the 38s, I can bracket the no logo years. 281785 shipped in August 1917 with no logo and 384433 shipped in May 1921 with small logo left side.
Engineering changes and other research for this issue is also available. WWI outbreak meant that the factory was basically under the control of the US Government for the duration of the war and to speed up production, manufacturing processes were skipped including logo stamping.
No-Logo" guns, all models mid-1917 to mid-1920
. . (K frame 38s - around 255,000-338,000)
. . (32 Winchester guns ran from around 50,000 to 90,000)
Small logo on left side ran from mid-1920 to 1936