Yes, Woody uses Windsor. Still, up until 1960 most film titles were hand lettered. They were easier to produce that way. Until photo- and digital composition, type was generally restricted to printing on paper.
Some lettering styles are based on typefaces, but most styles come from techniques passed down from masters and manuals in calligraphy and signpainting. Lettering was also commonly taught in art school. It was (and still is) a discipline distinct from typeface design.
I agree with Jan that what you have here is a very nice example of hand lettering. Look at the huge variation in each letter ‘a’, for example. The best way to get this look is to hire a lettering artist. If you have to use a font, check out Marcia and Surveyor, typefaces inspired by this kind of lettering.