Fat Cat or Bald Cat?

Would you rather have a fat cat or a bald cat?

I know its winter not by the calendar, not by the position of the sun, but by the fact Yumi now is sporting several bald patches on her back. She yanks out her fur this time of year, I think because of dry, itchy skin. She does not have fleas.

I've decided to begin adding fish oil to her kibble once again. I did this last year and it seemed to help

She will not eat wet food, (unless its the expensive smoked salmon I bought for my husband to enjoy.) She prefers to eat dry kibble and due to her previous food allergies, I always try to give her grain free cat food. She's currently eating Taste Of The Wild, but because its a dry kibble food, I don't think it gives her enough fat to keep her skin from drying out this time of year.

She's already over weight. We always measure her food so she doesn't get more than she's suppose to have, but this grain free food is not exactly low calorie. Plus, this time of year she wants more, to keep warm I believe. (We keep our thermostat set to 64 and use lots of blankets.) She's currently being fed 1/4 cup in the morning and 1/4 cup at night.

I hope the added fish oil helps her. She's also been taking hairball treatment fish oil weekly. Her fur is nice and bunny soft, but she does have dry skin dander, especially on her back. I brush her regularly to help oils distribute. I don't know what else to try. Hopefully she'll stop yanking out her fur.