I have SAD myself, and in the winter my symptoms are really really bad.

The cause of SAD is known in not getting enough sunlight, In winter the sunpower and the amount of light is low. This affects our biological clock, Some hormones like Melatonin also regulate this.

When in the evening, Melatonin causes you to be sleepy (when Melatonin level is high) . Some people make much more Melatonin when it's in wintertime. That's giving all kinds of problems and give these symptoms. Sunlight usually makes you feel awake in the morning, Because sunlight causes Melatonin to drop in amount. This does not happen with you and me. You feel not awake, and do not wake up because the levels of Melatonin are not dropping down enough for us to wake up and feel good. Medicine or tackling the depression is NOT the solution because it's the sunlight that does it. I can only recommend to get more sunlight throughout the day, maybe wake up more early?. There is something called light-therapy also, where you sit in front of a light for a few hours a week that emulates less strong real sunlight. You don't want to watch straight into it, but the light has to go through the eye (otherwise it won't work). So that is another option.