First: I have a problem with what I see as an implicit assumptions in the question that primitive peoples were simpletons. To understand the phenomena of midnight sun only a few straightforward facts need to be recognized:
- Time can be measured.
- Days are longer in summer and shorter in winter.
- The variation in day length is more extreme as you approach the poles.
As soon as the measurement of time is possible in a culture, and individuals of that culture are capable of travelling substantial distances north and south, the second and third facts will be observed. As hunter-gatherer societies such as the Inuit, Aleut and Suomi meet all these criteria, we have no reason to believe that the following deduction was not made.
- Far enough north (in NH) the sun will not rise and set during the longest days in summer and the shortest days in winter.
- Far enough south (in NH) the sun will always rise and set, even during the longest days of summer and the shortest days in winter.
To address the challenge that primitive peoples "didn't travel that far in a lifetime":
The Caribou Inuit rely on the Caribou herds of Northern Canada exclusively, and follow them on their migrations across the height of the Canadian Far North. These migrations cross the Arctic Circle, from Hudson's Bay to the far reaches of Ellesmere Island, and occur semi-annually, in spring and fall.
Similar caribou migrations occur across the height of Eastern Alaska, and of reindeer herds followed by some of the Suomi people in modern Scandinavia and Siberia.
The question makes a deep assumption about the day-and-night pattern above the Arctic Circle that is invalid. This article on life in Tromsø, Norway, where the “Polar Night” lasts all winter, paints a more accurate description:
Over the following months I learned firsthand that, far from a period of absolute darkness, the Polar Night in Tromsø is a time of beautiful colors and soft, indirect light. Even during the darkest times, there are still two or three hours of light a day as the sun skirts just below the horizon, never fully rising. During the longer “days” of the Polar Night, in November and January, the skies can be filled with up to six hours of sunrise and sunset-like colors.
The detailed pattern of day and night is different above the Arctic Circle, but not in a fundamental way. The 24-hour cycle remains intact, just different in degree thnn what would be experienced a few hundred miles further south.