Apropos of James Watson's imitation of Tatu Vanhanen, Alterdestiny and Lawyers, Guns and Money cite the case of John Svan, a Finnish immigrant to the United States, whose petition for citizenship was opposed by the US government on the account that he was "a Mongolian" and thus ineligible due to the Chinese Exclusion Act.
A spot of googling reveals that the judge was one William A Cant from the fair state of Minnesota. Luckily for Mr Svan and a sixteen other Finnish immigrants who had been denied citizenship, Judge Cant determined that "[i]f the Finns were originally Mongols, modifying influences have continued until they are now among the whitest people in Europe."
In 1911 the congressional Dillingham Commission produced a Dictionary of Races and Peoples, which addressed the Mongolian question thusly:
Finnish immigration has been larger in recent years than that of most other races having so small a population. It is practically confined to the Western Finns or Finns proper. These are Caucasian rather than Mongolian in appearance, while the Eastern or Volga Finns, who are not known to come as yet to America, show distinctly their Asiatic origin. They are divided from the Finns proper by a broad band of Great Russians which extends through Central Russia from north to south. The Lapps and Samoyeds, another very different stock, may be called the "Northern Finns".
[...] Until 1809 Finland was a part of Sweden, and before the dawn of history the Finns and Swedes were no doubt intermingling. This will account in part for the prevailing blondness and European cast of countenance amongst the Finns, which has led the Bureau of Immigration to put them into the "Teutonic division" of races. But the entire Ugro-Finnic stock seems to have been, in origin, lighter in color than most other Mongolians, perhaps as a result of their northern residence. Formerly they were taken out of the Mongolian grand division by certain ethnologists and put into a separate division of "ailophylian whites". Whatever their original stock, the Finns of Finland are today the most truly European of any race possessing a Mongolic speech, and in some respects their institutions are abreast of any in Europe.
"The most truly European of any race possessing a Mongolic speech" - take that, Hungarians!
This excerpt (PDF) from History of the Finns in Michigan by Armas K E Holmio provides a lengthy look at the origins of the idea of Finns as Mongolians and theorizes on why the notion persisted in the United States even after it had been discarded in Finland.