Far as I recall ( searching back to things I read from 1962 on ) the prevailing winds, especially at high levels, are rather constant- and head our way!
The level of the burst affects the quantity of fallout, but since the fireball ( unless so deep that it stays underground ) reaches the stratosphere, hot stuff gets all the way to the jet streams and is carried by them.
While a nuclear exchange between these two would certainly not be desirable, here is something to put it in perspective:
To: Francis
Of the 2,044 nuclear weapons tests worldwide, there have been 711 in the atmosphere or underwater: 215 by the U.S., 207 by the Soviet Union, 21 by Britain, 45 by France and, 23 by China.
The last atmospheric nuclear weapons test occurred on 16 October 1980 in China. The first was on 16 July 1945 in the U.S.
It is estimated that the total yield of all the atmospheric nuclear weapons tests conducted is 438 megatons. That's equivalent to 29,200 Hiroshima size bombs. In the 36 years between 1945 and 1980 when atmospheric testing was being conducted this would have been equivalent to exploding a Hiroshima size bomb in the atmosphere every 11 hours.
Stay Safe !