If Greenland is bought expect a heavy US buildup of forces to happen there.
You are going to have airfields for fighter aircraft, ASW aircraft, perhaps even strategic bombers there. Sub pens and a naval bases are very probable too.
Perhaps Reagan will try to put IRBMs in Greenland too in order to project power and threaten Soviet facilites in the Kola Penisula.
The SOSUS network gets a tremendous boost and the Soviet fleet is practically confined to the North Sea. I just don't see how they are supposed to get their subs through, now that Iceland is in US hands. That has a major influece on Cold War doctrines, since the US now practically has the unopposed ability to bring over reinforcements to Europe. Perhaps the Soviets realise that striving to tilt the balance in the Atlantic by a major surge of the Soviet sub Fleet into the Atlantic in case of war is unrealistic and they will never have the chance to stop the US convoys from making it to Europe?
Then either:
1. Abandon the big sub building programmes and rather focus their resources in building a bigger land army and air force, so they can conquer Western Europe, before the US reinforcements come in?
2. Focus more on tactical and strategic nukes?
3. Try to project their influence more in Africa, South America and the Caribbean Sea, hoping to install communist regimes there, that will allow basing Soviet subs and aircraft on their soil (thus bypassing the GIUK gap)?
Furthermore Iceland becomes a lot more attached to the US, with the US influence increased in the area. Who knows, perhaps later on the people of Iceland may even opt to join the USA?