Nope, several non-Southern states had segregation laws intact before Woodrow Wilson became president. South Dakota and Wyoming are good examples of this. South Dakota had a law intact starting in either 1809 or 1909 (either way, Woodrow Wilson was not president yet). Wyoming had one since 1887 (and that's when a New Jersey man was president). So it would be a brainless thing to suggest segregation had anything to do with the South. Montana had one starting in 1871, and Grant was president. And so on. Kansas had one before segregation
Oklahoma had one in 1903.