The chances are your dog is suffering a slight deficiency of the fat soluble vitamins ADEK as it is common for dogs on dry diets to have a harsh coat and the nose seems to show it first. I know what the bag says but it doesn't always suit the dogs. It you have access to raw bones this helps not only their teeth but also their diet. Also a tin of pilchards in tomato sauce goes down well, cheaper than tinned dog food. Scraps from the table, no cooked bones, added into diet and if they will eat fruit go for it. If you have a roast some of the gravy over the biscuits. The occasional raw egg. It is going to take you at least a month to start seeing an improvement. When I am gralloching the dogs line up for what is going although too much lights can give them diarrhoea, If you wish to discuss further pm me