The official stance of most Swedish governments during the Cold War was that Sweden was a non-aligned neutral in the contest between the superpowers. Swedish neutrality became an article of faith for most Swedish political parties, especially the Social Democrats. Sweden had not only sat out both World Wars, but its last official war was fought in the tail end of the Napoleonic Wars. Non-belligerency thus had a very long tradition in Swedish foreign policy as did the promise that Sweden would defend its neutrality with force if an outside nation tried to occupy it or otherwise trample on Swedish sovereignty. However, political declarations of non-involvement are one thing and actual policy is another. This is exemplified in the Swedish involvement in the Cold War. Sweden may not have been a NATO member, but it did "lean in" towards the Western coalition on a number of matters.
Some of Sweden's involvement with NATO was in the form of semi-covert sharing of defense plans and intelligence estimates by the Swedish military and NATO. Defense attaches or diplomatic envoys from NATO countries would periodically share intelligence and their Swedish hosts would likewise share information on Swedish capabilities. Sweden also restructured much of its defense in the 1950s and 60s to meet NATO requirements. There were connections between NATO and the Swedish air force so that the Swedes could communicate directly with NATO aircraft should the balloon go up. By the same token, Sweden enlarged its runways and air bases so they could in theory accommodate American bombers.
There were limits to such cooperation between NATO envoys and Sweden's government and armed forces though as it was a danger to be exposed publicly. This was one of the reasons why various NATO leaders never openly called for Sweden to join the organization; they recognized that it would both be a hard sell for the Swedish public and it would antagonize the USSR.
The other, and somewhat overlapping, option for Sweden was to engage in bilateral or multilateral defense relationships with various NATO members. This meant that Sweden was not really dealing with NATO, but with the UK, Norway, or the US. But the overall pattern of these relationships shows that these relationships were a near- de facto membership in NATO. The 1960 US defense policy document NSC 6006 contended that Sweden was a "functional ally" of the US, and by extension, NATO. NSC 6006 also affirmed the US decision to sell Sweden advanced weaponry like the Falcon and Sidewinder air-to-air missiles as well as advanced radar and other early warning equipment that could be used against the Soviets. The US and other NATO countries invested considerable efforts in building up the Swedish air force so that it could be used as one of the linchpins of Scandinavia's defense against the Soviets. Saab's various Cold War fighters were advanced planes, but they were not wholly indigenous either. The radars, avionics, and engines of fighters like the Viggen or Draken were often licensed versions of NATO-produced products such as the Pratt & Whitney JT8D jet engine.
The non-Swedish origins of these components occasionally posed a hurdle for Swedish defense exports of Saab jets as the license agreement imposed a degree of red tape for their wider sale. This had led to griping within Saab and other corners of Sweden of the self-interested nature of NATO countries' involvement within Sweden's defense. The various defense relationships were also not without their frictions either. There was a small but not insignificant faction within the Swedish state in the 1950s and early 60s for Sweden to develop its own nuclear weapon. The Swedish National Defense Research Establishment (FOA) did run a parallel research program into nuclear weapons with the Swedish Atomic Committee (AC). The AC was responsible for research and development of nuclear energy, but FOA also dabbled into producing dual-use reactors and processing-plants.
For its part, the US government was adamant in its opposition to a Swedish bomb. There was a fear that a nuclear Sweden would not only mean it would no longer need to cooperate with NATO, but also it would encourage nuclear proliferation. The US Atoms for Peace program try to provide Sweden with nuclear technology and fuel that could not be easily adapted for military purposes. The fear of a Swedish bomb also provided a reinforcement for the US to provide Sweden with high-end military technology with the logic being that the safer Sweden felt about its defense, the less likely it was to opt for the nuclear option for Swedish defense.
But the lack of a Swedish bomb was more than the result of US counterpressure. There was a strong domestic opposition to nuclear weapons in Sweden that coalesced in the late 1960s. Social Democratic Prime Minister Tage Erlander signed the Non-Proliferation Treaty in 1968 which was a public about face by the Swedish Social Democrats against nuclear weapons while the party had been slightly more supportive of their hypothetical deployment in the 1950s.
Ultimately, the nuclear issue underscores the key aspects of Sweden's non-involved involvement with NATO for Swedish politicians. The country could use its strategic position in Scandinavia to leverage equipment and intelligence out of NATO members that other neutrals could not. Non-alignment also ensured that Sweden had the option of sitting out a general NATO-Warsaw Pact war. This was also a double-edged sword as it also meant Sweden's tilt towards NATO meant it might be under Soviet cross-hairs anyway despite its official neutrality. Various sub scares in the 1980s in which Soviet submarines were allegedly penetrating Swedish territorial waters highlighted the dangers of these relationships. By the same token, Sweden's position in the post-Cold War NATO defense hierarchy became even more ambiguous than it was in the Cold War. Non-alignment is still a major component of Sweden's foreign policy, but it does now directly participate in NATO exercises and it was one of the larger contingents for KFOR's peacekeeping in the Balkans. But non-alignment is such a major domestic and inter-European shibboleth that it is very difficult for Swedish membership in NATO to gain substantive traction beyond various op-eds and think tank policy papers.
Sources
Aunesluoma, Juhana. Britain, Sweden and the Cold War, 1945-54: Understanding Neutrality. Basingstoke: Palgrave Macmillan, 2003.
Berdal, Mats R. The United States, Norway and the Cold War, 1954-60. Basinstoke: Macmillan, 1997.
Cottey, Andrew. The European Neutrals and NATO: Non-Alignment, Partnership, Membership?. London: Palgrave, 2018.
Jonter, Thomas. The Key to Nuclear Restraint: The Swedish Plans to Acquire Nuclear Weapons During the Cold War. Stockholm: Palgrave Macmillan, 2016.