I don't think it's anything to do with the season, since as far as your turtle is concerned, things are pretty much the same in his/her tank with the heat lamp and UV light.
By the way, if you'd like to know whether your turtle is male or female, go to
http://exoticpets.about.com/gi/dynamic/offsite.htm?zi=1/XJ&sdn=exoticpets&zu=http%3A%2F%2Fwww.austinsturtlepage.com%2FInfo%2Finfo.htm
and that will give you a pretty good idea.
How does he look otherwise? You said his eyes were alert but he sleeps a lot. Do you ever notice any bubbles coming out of his nose when he breaths? That's usually a sign that there is some sort of respiratory problem. When my turtle is basking and something startles him, he pulls his head in really fast and it makes a high pitched squeal when he has been stuffed up. This is another clue if we haven't noticed his nose bubbling. Try keeping an eye on your turtle to see if you notice any signs of respiratory problems.
Another reason why a turtle would stop eating is if it is constipated or impacted. Of course, if he hasn't eaten for a while, he probably hasn't pooped for a while. If you suspect this could be a problem, or want to give this a try since it can't hurt, you can soak your turtle for 30 minutes in warm water that is chin level. Warm is what feels comfortably warm to you and you know won't be too hot for your turtle for 30 minutes.
How long has it been since your turtle has eaten? What kind of food did he eat before, and how active was he?
Why don't you check him carefully for any upper respiratory symptoms. If you don't see anything, try the warm water soak. Let me know after that, and we can see where to go from there.