Good question, Doc. It's one I've actually had posed to me quite a few times and people generally ask why we don't rely on France, the UK or even the US who stations troops and equipment in Norway and the answer is simple - they aren't in a position to defend Norway, Sweden or Finland or the smaller EU states (a combined NATO force defends the Baltic nations. This is known as the Enhanced Forward Presence initiative. Norwegian forces are part of the eFP in Lithuania).
The UK and US are around frequently, but their equipment is some 1600km away from our principle adversary Russia at the closest, in long-term storage in underground facilities pockmarked throughout the Norwegian countryside. Their equipment isn't really made for fighting in Norway either, but is stored here for deployment elsewhere in Europe such as Poland, Latvia, Estonia or Lithuania. No naval or air force assets are assigned to the US contingent in Norway, but the USAF and USN do frequent our air and waterspace for major exercises (several destroyers, submarines and on occasion P-8MPAs and Nimitz class carriers, but never in large numbers). The UK doesn't have any assets in Norway permanently, but their Royal Marines train in Norway on a yearly basis for cold weather training, as do the US Marines.
Norway actually borders Russia, but at sea and on land, and with the closest allied forces over 1500km away from that border and undersized and under-equipped to fight Russian forces in Norway, rather being used to reinforce a combined NATO force on mainland Europe, it's incumbent on Norway to fight for Norway. This is the Norwegian-Russian border, shown from the Norwegian side. It's mountainous, forested and our countries are separated by two rivers along 2/3s of the border providing a natural barrier from one another and blunting the threat of an armored or infantry assault (Norway places greater emphasis on air and sea control).
While Norway's Army isn't strictly for fighting in Norway, being currently deployed in Mali, the Sinai, Afghanistan and Iraq, the Norwegian Border Guard and Norwegian Home Guard provide the bulk of our homeland defence against external threats. They operate heavy armor, air defence assets, naval and air units too, and act as an extension of the Army when necessary.
But while there are forces to defend cities and our land, our primary threat doesn't come across our shared land border. These photos of the Russian Navy were taken by the Royal Norwegian Navy and Air Force in the Norwegian Sea as they were en-route to participate in the Russian intervention in Syria.
The Russian Northern Fleet - complete with multiple ballistic missile carrying submarines, numerous nuclear and DE attack submarines, a Kuznetsov and a Kirov class backed by additional destroyers and ASW frigates, not to mention the sizable 51st Kirkinesskaya Red Banner Marine Brigade, and 317th and 318th Marine Battalions of Russian naval infantry.
That's our enemy and it's a sizable one. We accept help from our NATO partners, the UK and US mainly, especially as part of Standing NATO Maritime Group 1 which is comprised of Baltic and North Sea nations (meaning Turkey, Italy, France and others aren't part of it, but contingents of SNMG 2 instead), but as their contribution to Norway's defence is limited we have to do our part to keep the Russians at bay as our partners will do for their countries too.
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Sweden doesn't border Russia, but it has a standing army just in case. It's Air Force is sizable, but its navy small (35 ships, half patrol boats versus 70, the majority large armed OPVs, for Norway). Finland does border Russia and has a large air force and army as a result, but it's navy is smaller and focused mostly on harassing Russia in the Baltic with mine-layers and light corvettes. While Sweden's national defence strategy is to be able to defend itself, Finland's is that any conflict with Finland will spill over and involved NATO, and its navy's size reflects this, meant to slow down Russia while allied forces from the rest of Europe mop up the Russian Baltic Fleet.
Iceland doesn't have a military and is instead defended by a combined NATO forces of mainly Canadian British, American and Norwegian forces. Germany, Italy and France all provide a smaller level of support alongside the Czech republic, Denmark and Portugal.
Denmark is somewhat in between Sweden and Finland in terms of overall capabilities, also facing the threat of the Russian Baltic Fleet.