I guess the Cold war might have been a bit more likely to turn hot.
If that happened it wouldn't have made that much difference. Alaska has some valuable oil resources but aside from that it isn't a core part of the United States.
Paljoey: in case you aren't aware, Russia colonised Alaska (its very near to Sibera and during winter (I think?) the sea between the two can freeze over). US bought the territory from Russia (very simliar to Louisanna purchase).