I would hope to think it's frost damage, however all the plants are inside. The first plant to get it was based near a radiator, the larger other plants are on a large window sill and although the radiator below it is not on the windows have triple glazing and at the moment about 19 hours of light.
I'll do two things, I'll move all the plants back to the warmer window that has not much natural light but more radiator warmth. I'll trim back the seemingly infected areas, then I'll do as scoville suggested and let them dry out. No idea where to buy distilled water in Finland though, so perhaps a boil and cool will do?
Then if still no improvement, I'll also cut back all of the plants to stumps. Only 4 of my plants managed to start producing chilis before this set in. They are all turning starting to turn red now. I'll make sure I don't keep those seeds for future use but will use for cooking, but I will wait for them to go red before cutting back.
It's worth noting, those that are producing chilis, Chi-Chien, Purira and Bhut Morich seemed to be affected last, although one of the plants (the one with the chili fruit photograph) that I grew from an Indian seed is the worst affected.