Some people add lights and some don't. I don't light my coops to a) give my hens a break if they need one, and b) no electricity in coop.
If you do add lights, do not keep them on all day and night. They need some darkness in their night time. Add light to give them a 15 hour day of...
She may be getting ready to do a minor molt. I've had several 9 month old pullets molt. It's generally not as bad as a full molt. Look for her tail feathers to be missing.
Cold has nothing to do with it, chickens are very well adapted to the cold. (they have a harder time in the heat)...