Why did the first people to settle in very cold climates decide to settle in such a harsh climate?

My assumption: like with any territorial animal, to avoid competing with other tribes over resources. And apart from the very very cold places like Greenland, most cold places actually are abundant in food when spring comes, which would be the time tribes would venture further north in cold climates.
- Yep.
  And it's not like someone went from Africa to Greenland on a walkabout.
  It took generations for that kind of migration, some people decided they went far enough and stopped. But at every stop, the ones who could handle colder would expand North/South where there's less competition.
  They were repeatedly being selected for the people who could handle a slightly colder environment, so by the time the population reached the polar regions, all that was left was people with traits to handle the cold. Any remotely beneficial recessive gene would quickly replace dominant alleles in the population.
  People think of evolution as spontaneous mutations, but really it's just the concentration of recessive genes that have been around basically forever
  
  They were repeatedly being selected for the people who could handle a slightly colder environment, so by the time the population reached the polar regions, all that was left was people with traits to handle the cold. Any remotely beneficial recessive gene would quickly replace dominant alleles in the population.
  Although I'm sure there was some genetic adaptation, I'd argue it was more technological advancement. The northernmost tribe discovers a better make of clothing, or a better housing structure and suddenly the colder winters farther north are now tolerable so people settle there. The new northern tribe refines their technology and knowledge and now that they know how to... ice fish or something they have a winter food source, and now their descendants can settle even farther north.

My guess would be that it happened gradually. Someone living in a place where the minimum temperature is 15 might be willing to move north to a place where the minimum temperature is 13 as long as other factors are better for him. Couple of generations later you have someone who's living in a place where the minimum temperature is 13 willing to go north to a place where the minimum temperature is 10, so on and so forth.
- It happened even more gradually.
  Your kids moved out of the house when they were adults and built their own, a mile over the next hill north, cause the other good spots were taken. Repeat x 10000 and you've "migrated" all over the globe.

As a Finn, I've often wondered about the same thing. In the summer the air is filled with mosquitos and in the winter it hurts your face and lungs yet some people were like "yep, we'll settle here"
- Maybe all the people south at the time were assholes with pointy sticks.
  
  Indeed, they're now called Slavs and Germanics.

The current era of excess is unprecedented in the history of the world. For most of human history, starvation was a serious threat and hungry people would go anywhere where there was food that wasn't already claimed by someone stronger than them.
(The people in very cold climates would fight to defend their resources too! Ultimately there was no unclaimed land that people could survive in, except after major catastrophes.)

Because they weren't necessarily always harsh, cold environments. The global temperature has fluctuated significantly in the last 1000 years or so. We had a medieval warming period from about 1000AD through 1200AD, followed a couple hundred years later by a "little ice age". Technically, our world is still in an ice agethough the last 12,000 years or so have been remarkably stable compared to the longer scale geological timeframes ice ages generally span. Good thing our dependence on fossil fuels has upended our real handy metric for tracking this kind of stuff so we now have basically no clue wtf is going to happen climate wise in the next 10,000-12,000 years. Warhammer 40k is very optimistic about humanity lasting that long.

"Boy there sure are a lot of people around here. It's getting kinda hard to feed all of us and there aren't as many animals. What if some of us just went like 20 miles thata way?" (points north)

Competing with ice and snow can be far less stressful, dangerous, and depressing than competing with other humans and tons of other species.

We basically spread to everywhere that could support us. If there was food, people lived there.

There have been some good responses…
I’ll add my poor one.
Adventurous people, wanting to be away from others would also weigh in.
As above no one moved to Norway from the Fertile Crescent.
People had to figure out clothing and fishing and hunting and farming then how all those things we different as they move further north. James Burke, in Connections points out how the plow changed. In light sandy soils a stick works, but in heavy wet clay you need heavy curved iron plows.
So. Why? Because Bob smells, and never cleans up. We’re outta here — but over 10000 years give or take.
- I think you're on to something; I'm an introvert norwegian, and I'm a social recluse even by norwegian standards. I'll take sideways sleet any day rather than risk being spoken at.

Not only cold. Without AC the south of USA would be completely different too.

Get away from assholes ?

Hunting seals and whales in some cases, as in Alaska.
- Yep, following food.
  Or, it wasn't as harsh when they first appeared. I mean there was the Little Ice Age in Shakespeare's time, where the Thames froze over. If you took that as a sign it was becoming permanently like that in London, what would you do? It's not like you have somewhere else to go that you know it's better (or hell, where anything is).
  People in the 20th century easily forget how little knowledge the average person had even 100 years ago. Hell, even the information the wealthy had. Just a couple hundred years ago a globe of the earth was practically priceless. They were still a luxury in the early 20th century.

It's a good point that competition can drive animals to areas they wouldn't choose. But it's also true that pioneering a new niche can lead to animals thriving rather than just surviving.

I've heard the argument somewhere that allergies may have had a say. If someone was allergic to local flora/fauna it creates a force to push humans outside their traditional living places. I'm not sure how true it is but it resonates.
- To add to this, social relations are a driving factor as well. Family Feud? Just move the family!

My understanding is that we are currently living in an interglacial period.
I believe the pattern on Earth recently has been you get these relatively mild climates that last around 10 thousand years, in between 100 thousand years of ice age.
So, maybe the climate was harsh pretty much everywhere that wasn't the equator for most of time our species has existed.

Many of the northern settlements were escaping war, pillaging, and plundering.
Also the climate may have been a bit less harsh one thousand years ago

I imagine following migratory animals may have something to do with it.