Is my cat's dry skin and vomiting related to her diet?

Usually this winter hair loss is a result of environmental dryness. I would be topically moisturizing her skin daily with fatty acids using a spray such as Hy-Lyt moisturizing spray. I would also advise starting her on some systemic skin supplements such as Vitamins A, E, Zn, Biotin and fatty acids. These are all present in the product EFA-Z+ which you add to the food. In addition, because of her age, I would also advise having your vet do a geriatric screen to rule out any other systemic diseases such as hyperthyroidism which could be causing the vomiting. As far as diet is concerned, many cats can tolerate wet food, but not dry. Have you tried stopping the dry food?