Why should this region be any more humid, gloomy or foggy than Warsaw, which is two hours west?
Actually, it's the least foggy area in Poland, as it is the area that receives the least inflow of warm, moist air from the Atlantic, North Sea and Baltic, as opposed to Szczecin.
than Warsaw, which is two hours west?
Warsaw is on the extreme Western limit of this range, and gets some occasional winter protection from warm maritime land masses. Białystok, though only two hours way, doesn't.
Also, Arctic air masses coming from the North are somewhat tempered as they flow over the Baltic before they hit Warsaw. Not so much with Białystok.
Yes, Białystok is the coldest city in Poland in winter, and sometimes gets cold snaps that do not penetrate into the rest of the country, even nearby Warsaw.
That said, no, the difference between Białystok and Warsaw is usually not extreme, and the stories about polar bears and penguins and five meters of snow are, of course, silly. The difference between Białystok and Wrocław, the warmest city in Poland, on the other hand, can be quite large.
Also, about the "two hours from Warsaw" bit, you have to view geography through they eyes of people from Polska A, who consider places like Białystok, Lublin and Rzeszów are very distant from the rest of the country, regardless of actual travel times. A lot would be surprised to find out that Białystok and Lublin are actually closer to Warsaw that Gdańsk, Poznań, Wrocław and Kraków are. Also, in their mind, they place Warsaw a lot more to the west than it actually is, about where £ódź is, and Kraków somewhat more to the West, where Katowice is. And Białystok where Suwałki is, or even Sejny, right on the border, not far from Minsk.
We had a doctoral student from Białystok in our department in Skierniewice, and the other students used to tease him about being from Vladivostok and saying hello to the Tsar, Putin or £ukaszenka when he went home for Christmas (by horse-drawn sled, of course).
There's no bad weather; just bad clothes.
Very true.