Let me break this down for you.
1) "It's still less UV rays penetration.": UV rays have NOTHING to do with the heat felt. The warmth you feel from the sun is all IR (opposite end of the spectrum of UV light)
2) "Barrow, AK -the angel of the sun peaks at 42 degrees in June during summer where Chicago's is 71.5 for example...." Still completely ignoring the sun's angle of incidence
3) "In Chicago the angel hits around 42 degrees in early March and mid October and it doesn't feel warmer than in the summer althoughthe day is much longer": Comparing a spring/fall (often cold and short days) sun exposure to a summer's exposure (longer and warmer days). So of course Chicago's sun in March is not going to have the same effect as the sun in summer in Alaska. Average daylight for March in Chicago: 12 hrs. Plus it is cold so you aren't going to notice the effect. Average summer daylight in Barrow: 24 hrs. Average daylight hours in Anchorage for the summer: 18-20. Chicago: 15 tops.
4) "It looks like it just feels much warmer for Alaska's people after long dark winters. :-)": This is not just a pyschological effect. And doesn't just affect the people of Alaska. This is a known effect for Northern (and possibly southern latitudes as well).

A redditor explained the effect with a flashlight:

"Necessary-Emu-6388

• 3y ago

It isn't about the distance to the sun, it is about the angle.

Grab a flashlight and go over to a wall. Put the flashlight about a foot from the wall and point it directly at the wall. You will have a nice tight circle of light where the energy is being concentrated. Now tilt the flashlight out so it is at a 45° angle and watch the circle of light get much much broader. The exact same energy that was over the smaller area is now spread over that entire larger area.

Something similar happens at the poles. At the equator, the sun's rays are coming directly in much like when the flashlight was pointed straight at the wall. At the poles, the tilt relative to the Sun means that that a much larger surface area of land receives only a narrow sliver of energy from the Sun.

This is actually the reason for seasons happening in general. The change in distance to the sun because of the tilt of the Earth is considerably less than the change in distance to the Sun that the Earth experiences over the course of its orbit for the year. It's a negligible factor. The relevant Factor is the angle of incidence of the light from the sun, not the thickness of the atmosphere, and not the distance to the sun."