Suppose I owned a small airplane and lived in a remote town in Alaska in 1986. Could I fly into the Soviet Union, land near a town, and return to Alaska without being noticed? What sort of security or military presence would I need to evade to make the trip, and how risky would it be?

Okay, finally a question that I'm probably one of the few people qualified to answer. My historical background is just a BA and MA in history, writing primarily on US Army Air Force bombing campaigns in WWII, with particular attention to targeting of civilians - I know, not what we're talking about, but just letting you know I'm one of you but am writing a bit outside of my academic wheelhouse. Professionally, I am an Air Force pilot and have flown against Soviet era AAA and SAM systems across the world, admittedly mostly against ancient ones with poorly trained operators. I will make sure I don't violate rule 4 with "personal/anecdotal" experience by backing myself up with sources, which is good practice anyways because if I write about stuff that I do at work, I need to make sure it's already on there so I don't embarrass myself like this.

Caveat: My training in counter SAMs / SEAD (suppression of enemy air defenses) began in 2014, not 1986, and even then, it was the basics - I don't specialize in it, I don't fly F-35s or F-16CJs like my Wild Weasel brethren that live for this. I'm using old copies of Jane's, which are available to me through a subscription I have from work - these are not classified, but are behind a paywall. Jane's has been the gold standard of quantifying and comparing military equipment across pretty much every category - aircraft, planes, weapons, etc, and has been since the late 19th century. The oldest copy of it that I've touched in a 1898 edition of Jane's Fighting Ships in the stacks at Air University's library in Maxwell Air Force Base, Alabama. While it is a western publication, I'm using references across the years to get more accurate data. Of course, newer systems are less likely to have accurate data, and data gets more accurate as Soviet client states broke off and allowed western intelligence to analyze the systems or they were seen in combat and western intelligence extrapolated based on their performance.

Assumption: You mentioned a small airplane, but did not specify which, so I will fill in. One of the most ubiquitous US civilian airplanes is the Cessna 172 Skyhawk. Anecdotal, but it is also the first plane I ever flew, and probably the first for the majority of American pilots. It's an almost 70 year old plane now, so it would be available for your hypothetical flight.

Data and Methodology: First, a quick term to explain - radar cross section (RCS). This is a measurement of a plane's reflectivity on radar. It's based off the material, shape, size, and smoothness of a plane's surface. The Cessna 172 has a RCS of 10m^2 worst case. Worst case means with the nose of the aircraft pointed towards the radar. To compare this with other planes of its day, an F-14 Tomcat would have a 25m^2 RCS, an F-15C's is 20m^2, an F-16's is an impressive 5m^2. Today's F-22's unclassified/estimated RCS is .0001m^2, roughly the size of a marble. Long story short, your Cessna would be measurable on radar if it was tuned to look for something like you.

Answer, kinda: Without getting TOO much into how radars work, typical Soviet SA systems are not on 24/7 unless put on alert, they rely on men located at the radar site, and there are several layers of both range and sensitivity across several different types of SAMs. Strategic SAM systems aren't sensitive, they're meant to pick up US nuclear bombers and send a heavy missile that doesn't need to maneuver to hit its target, so they have very high ranges. Tactical SAM systems can be sensitive, but their range suffers because their missiles are intended for fighters that can 'defend' via their agility and turns, so the missiles need to keep up. Go figure, I can't source any documentation of Soviet missile defense deployments in 1986, so I can't tell you if there's an ingress route or not with certainty. HOWEVER - I can make an educated guess based on sheer geography and military knowledge. The Soviet Union's entire eastern half is incredibly low density population-wise, and it's huge. Because they can't exactly make a wall of ZSU-23-4s across their eastern border, there are likely several gaps you could ingress into and avoid detection by flying nap of the earth (i.e., low). For more on Soviet air defenses, this 1989 article on anticipated Soviet reactions to US stealth technology goes into their organization.

The thing you'd have to worry most about is interceptors. MiG-25s or MiG-31s could be flying a CAP anywhere, and although big sky theory is a thing, depending on so many factors (their position, your position, your color, sun reflectivity, etc.), you could be easy to spot with their Mk. I Eyeball sensors (incredibly advanced, I know). Additionally, most interceptors have radars that can be a bit more sensitive to other aircraft since they don't have to worry about the ground. Can't find a good illustration for an aircraft of that era, but this one serves well enough for the premise.

ALL OF THAT BEING SAID, you can pretty much disregard it all, because as many aviation fans know, Mathias Rust was a young, 50 hour Cessna 172 pilot (for reference, 50 hours is about what I'd expect the most basic of private pilots to have before being allowed to fly without an instructor in the US) who took his plane from West Germany to Iceland to Finland and then landed directly in Moscow's Red Square. Unlike your hypothetical flight, young Mathias did not make a return trip until he was pardoned about a year later, but I think it's worth mentioning because he WAS picked up on Soviet air defense radar, he WAS intercepted by Soviet aircraft, and through various failures and breakdowns in Soviet C2, he made it through what was the most heavily defended and fortified air space in the world outside of the US.

To summarize, you probably could, but it would take a lot of precise flying, a pre-planned flight where you avoided populated areas and landed away from anywhere, and then returned without refueling (unless you have a perfect Russian accent and enough rubles to somehow arrange for AV gas to be transported to you), which would incredibly limit your options. Also, you're probably landing without a runway to avoid civilization, so I hope you're really good and can also find some dense ground that fits all of those conditions and is large enough for you to take off in.

For more on RCS: https://www.globalsecurity.org/military/world/stealth-aircraft-rcs.htm

MIT lecture on RCS: https://www.youtube.com/watch?v=a53Cg3KUTt4

One last edit: just noticed OP's username. Hope you're flying to Winterfell to decapitate Roose for The Ned.