If you mean 1960, then this is a later-emigrating group I am not much in contact with. If you mean 1860, then most of these people were part of the Mormon Church and settled in Utah. The group I am most familiar with left from 1875 to about 1914, settling in mostly Canada and the U.S. (north central and west coast).
Most of the customs still in practice revolve around the Christmas holidays. Not many of the descendants of the immigrants still speak Icelandic, except for older "Western Icelanders" in Canada. I knew of Christmas foods and customs, and of some of the Icelandic foods still prepared at other times of the year, like rolled, smoked lamb or liver. These meats were sliced very thinly and served on buttered bread (still are, in Iceland).
This is not a very complete answer, but I can perhaps provide you with better information if I know the years you are talking about. Most of the 1960's immigrants would likely be college students (many in North America for their college years, and of course some staying on due to marriages or jobs), and those already in a profession - diplomacy, university professor, medical, etc.