Whether it's sunny or cloudy makes no real difference because, if one has the right FS light bulb in the ceiling fixture of the room where the bird is kept, it's always sunny and bright in there (so much so that every morning I sing a song to the birds that I made up and it says: Good morning, good morning, the sun is out, the sky is blue etc etc because, to them and with the help of the full spectrum bulbs, it's always sunny in there regardless of how dreary and gray it's outside). The problem with the Northern countries that are near the North Pole is that there are no real seasons so the bird owner needs to set up a fake temperate climate schedule so all four seasons are represented by different lengths of daylight. If I lived in a place like that, I would sit down in front of a computer and looking up all the sunrises and sunset times of a temperate climate city, I would then write them down in a predetermined order - for example, I would put down something like this:
January 1 to 15 - turn on red lights (these are the ones that most resemble twilight) at 6:30 am, turn on FS lights and turn off red lights at 8:30 am - turn off FS and turn on red lights at 3:00 pm and turn off red lights at 4:30 pm.
Then go on to Jan 15 to 31 moving the times by 10 minutes earlier in the morning and 10 minutes later in the pm - and so on and so forth. This way, there are different lengths of daylight every two weeks (which is the rough equivalent of 20 minutes of change in daylight in nature - this is because we know, through studies, that birds register a 20 minute difference a day of longer or shorter daytime). If it's done through timers and one is consistent in changing the timers every two weeks, it should work out.