It is unlikely that she has a thyroid problem, as thyroid disease does not cause itchiness. Hair can fall out with thyroid disease, and the skin can change colors, but there is no itching involved. The change in color to the skin is a common secondary reaction to chronic inflammation.
The first thing that is usually suspected in cases like this is flea infestation. Even though the weather has turned colder outside, the fleas have no trouble continuing to live inside of the house. The most common time of the year that I see flea infestations in dogs is in the fall, when owners stop applying the flea preventatives to their dogs. Even if you do not see any fleas on your dog, if your dog is allergic to the flea saliva (a very common allergy) then just one flea will drive her crazy. So, she (and any other pets in you home) should be on a safe and effective monthly flea control product like Frontline, Advantix, or ProMeris.
Flea infestation can be complicated by secondary bacterial infections, so you should bring your dog into the veterinarian to be evaluated for this. These infections can also be a primary problem. They are generally treated with long-term antibiotics, usually for about 6-8 weeks. In some cases, there can be a yeast infection as well. This is generally characterized by a smelly, greasy exudate on the skin, often with yellowish/brownish crusting. This can be diagnosed by the veterinarian with something called an impression smear, where a glass slide is touched to the skin and then stained and looked at under the microscope. If yeast are present they are treated with a medicated shampoo twice weekly for several weeks and then once weekly for several weeks thereafter. In particularly bad cases, an oral antifungal may be necessary.
Another common reason for intense itchiness is sarcoptic mange (scabies). This is caused by a microscopic mite that burrows into the dog's skin. The disease can be diagnosed by a skin-scraping in the veterinairan's office. In many cases, the mange mite is not visible with the scraping, so if the vet suspects scabies they will usually go ahead and treat for it. The treatment is a topical solution called Revolution that is applied to the back of the dog's neck once, and then again in 3-4 weeks. This disease can also be complicated by secondary bacterial or yeast infections.
Lastly, chronic itchiness can be caused by either food allergies or atopy (seasonal canine allergies). Many dogs who respond to steroids have a true atopy problem, and not really a food allergy problem. Food allergies usually involve scratching at the ears and rear-end, as opposed to the constant licking of the paws. Unfortunately, most dogs do require steroids and antihistamines to remain comfortable. For some dogs this period is only in the warmer months, but for many it is an all year-round problem. Most of my atopy patients are well-controlled on a drug called Temaril-P, which is a combination of an antihistamine with a small amount of prednisone.
There are other treatment options that do not involve chronic use of steroids. One that is easy to try is a straight course of antihistamines. Different dogs will respond differently to different drugs, so it may be the case that several antihistamines must be tried before the right one is found. The most common ones used are benadryl (diphenhydramine) and chlorpheniramine. Many dogs will not respond to antihistamines alone, and another modality must be added. The most common is to use a special shampoo designed for allergic dogs. Because allergens that affect dogs do so by landing on the dog's skin (instead of being inhaled, as they do in people), the allergies can be decreased with frequent shampooing with an appropriate product, such as Histacalm. Your vet can recommend an appropriate product for you.
Another option is allergy testing, either using a blood profile or intradermal skin testing. With either of these tests, the dog can be evaluated for sensitivity to specific allergens, and then a unique "vaccine" is made for the dog to treat these. The animal is usually given gradually increasing amounts of the allergy serum over the course of many weeks to months. This is called hyposensitization therapy, and has the least side effects of any allergy treatment. This works in about 67% of dogs.
There is a new drug available now for allergic dogs called Atopica. This is designed specifically for veterinary use. It can be very effective, and does not have the negative side effects of using long-term steroids, however, it is also quite expensive. If you are interested in trying this, you should talk to your veterinarian about ordering you some.
Food allergies are treated with an exclusion diet such as Hill's z/d or Purina HA. It can take up to 8-10 weeks for a dog to respond to this diet, and they must be fed absolutely nothing else.
I hope that this information has been of some help to you, and I wish you the best of luck with your dog. Please let me know if I can be of further assistance.