I think it might be fungus. It starts at the paws, then on and around the mouth, in the eyes and lastly around their genitals. It is very difficult to eradicate but possible. It is as you say worse in winter because of the wet grass. There is a website that tells you how to handle this but apparently it takes a long time to work. Persistence however is important for your pet. I will try and find the website and post the url here for you.