While the North Pole and Eielson areas aren't always colder than Fairbanks, that is often then case in the winter (when there is not a Chinook) and for summertime low temperatures.
First, even more so than Fairbanks, North Pole is a flat land with lots of old sloughs and channels of the Chena and Tanana Rivers that provide good places for cold air to pool.
Second, there hardly any human development to the east and northeast of North Pole, while to the northeast of the Fairbanks Airport is, well, Fairbanks City. This is important in winter because the prevailing drainage flow of air is from higher to lower elevations, which in both cases is (north)east to (south)west.
Third, the North Pole is in "collection" area for cold air draining down the Chena River valley and far from any significant ridges. This helps keep wind speeds in North Pole very low in winter. The Fairbanks airport, in part influenced by nearby Chena Ridge, sometimes gets more wind in the winter than North Pole, which allows for more mixing of air, which keeps it from being quite as cold as North Pole.