A Nordic Economic Community was on the cards in the 1960s/70s, as a Nordic version of the EEC. An NEC if you will. A fully single market built on top of the already existing Nordic Passport Union which granted freedom of movement for people (and fast-tracked citizenship!). Such a union might easily have come about; the two main reasons it fell through were Norwegian worries over Swedish industry dominating the tiny Norwegian industry (in the days before North Sea oil & gas, which would have easily balanced things out), and the Finnish-Soviet peace treaty (which funnily enough didn't stop the Soviets creating the Warsaw Pact, but it's not surprising the Soviets didn't see the terms as really applying to them, only to Finland).
If it's clear from any "Nordic Economic Community Treaty" that Finland at least will remain fully neutral and it's a primarily economic agreement, then I think you could perhaps swing it (and bonus for the Soviets you might get a fully neutral Nordic region which would be interesting for them). Part of the Norwegians desire was a 5-10 year phase-in process, allowing Norwegian industry to gradually acclimatise to the wider market and competition. That would also bring the time for oil & gas forward, which would balance the equation. I think you'd have a full single market, perhaps a unified currency, a Nordic Parliament. Similar to the EU, following the collapse of the Soviet Union, it would probably evolve in to a Nordic Federation, with closer links between the 4 military forces (none to worry about in Iceland...), co-ordination in much of foreign policy (reasonably easy considering the similar policy positions generally), etc etc.
Estonia would probably argue for joining, which if it was successful would probably be followed by Latvia and maybe Lithuania, but I think all three would be a bit much for the Nordics to swallow; they aren't really cultural brethren, have significant Russian minorities, and don't speak a Nordic language. However, I'd imagine the Nordic business groups lobbying for it as it would present new ground for business in.
Again, how do you convince Norway to go into a union with a country that they voted overwhelmingly to split from 40 years earlier? The scandinavians have very different internal and foreign politics. Integrating them into one state makes little to no sense from a cultural, historical, political or economic standpoint.
The Scandinavians/Nordics have different politics, but are cut from the same cloth generally. A similar general outlook on politics and society (the Nordic model / social democracy), significant neutral leanings even in Iceland and Norway which are NATO members, a desire to work together as evidenced in the 20th Century by negotiations over a Nordic Community and the latter Nordic Council in OTL, and even the Norwegian anthem refers to the Scandinavian three brothers. I think Norwegian concerns are more over being dominated by Sweden, rather than a desire to avoid any union. Similar to Ireland and the UK - Ireland has absolutely no wish to be ruled by the UK, but is happy to be in the same overarching union (the EEC/EU) with all it's benefits.