Or check out this nice mapping tool on the geographic distribution of last names in Germany (check out Carstensen, Hansen, Hinrichsen, Jansen, Janzen, Johannsen and Petersen).
Are you able to get that to work other than Germany, Poland, and the two counties with red-and-white flags to the south? You probably found this page and then encountered the same problem as I did. Although strictly speaking it's only the search that doesn't seem to work for the additional places (which are new. Last time I surfed that site, it had only the countries listed above.) There is a very similar tool on another website for Italy. Forget the address, though, but that one also has the US - but only by state.
Well Smit, obviously (and also Smid) is not German at all but Dutch.
And you totally forgot the South German spelling, Schmid! Oddly, people spelling the name like the word is spelled (Schmied) are not only relatively uncommon but distributed across the entire range of Schmidt and its regional spelling variants.
I'm much more amazed at the name's pretty complete absence in the east. Is there some east German dialect term for a smith that I'm not aware of or what?
Schmidt looked common across the east to me. On the relative frequency map it exceeds 2000 per million throughout.