Iceland knows that it’s likely the EU’s first moves would be to start dumping unvetted, unwanted refugees there.
Iceland could literally lose it’s identity overnight.
Since Poland and Hungary won’t take any, and Italy is plainly saying that they don’t want any more.
Iceland may want to stay in NATO. Putin may want to test his limits at sometime.
Norway is also in the EFTA and EEA, but they are quite Islamized in many urban areas, particularly Oslo. Iceland at least has the advantage of relative geographical isolation, and it would be up to Iceland’s government whether to go the route that these European countries have gone whether a full member of the EU and Eurozone or not.
Also, the EU would begin to strip away their ownership of their fishing grounds in the North Atlantic which is their primary means of survival.