Cod Liver Oil capsules (commonly referred to as "fish" oils since cod liver oil seems to be prevalent) are VERY high in Vitamin A. An overdose of vitamin A is toxic and can lead to organ dysfunctions. Personally, I only use Cod Liver Oil capsules if the dandruff/dry skin is absolutely unbearable, and even then, I use it sparingly.

My first suggestion is to not bathe frequently unless your shampoo is very mild and gentle and it HAS to contain conditioner (don't worry, most pet-specific shampoos are 2-1's). Otherwise, you're doing more harm than good by drying out the skin and coat further. Also, grooming is essential. I recommend you buy a Zoom Groom or some type of hound glove and rub your dog in a circular motion. This will release all the loose hair and dead skin cells while also stimulating the skin's natural oils.

You mentioned that your dog developed dry skin during Spring, or this time of year. My guess is that if his coat is glossy and shiny, it's not a nutritional deficiency or anything. I think it's an allergy to something in the enviornment. Hope this helps.