
First thing I would say is remember they are not really pure white dogs day in day out. ( see tip on Lavender talc for a miracle and simple clean up :-) )
General colouring can be a couple of things, acid and the other food/diet. James well beloved used to be a favorite of westie people but it doesn't seem to be now. Not sure if it changed somewhere along the way.
One thing I always say to people to find out if it is a food thing first and to find this out put them onto something like Butchers tripe for 4 -6 weeks solid forget the treats and tit bits see if there is improvement.
Be careful of shampoos, use good quality ( not pet shop types) Biogroom wiry coat shampoo is brilliant for terriers and smells suberb. Wash only 2 -3 times a year and make sure you rinse and rinse and rinse. Their double coats holds soap very easily and can cause itching.
My miracle tip ( not really a miracle) A fantastic product for cleaning them up a bit without bathing ( I give a tub to anyone who every buys a puppy) Is Johnsons camomile and lavender talc.
NOT any of the other ones. This specific one is made with pure corn powder ( Zea Mays) so is very gentle on the skin. I swear people around my walking routes think I am the clean dog miracle worker but I just give their feet a brush through with it when out on wet or muddy walks.
It is great to sprinkle on the feet around the mouth and head and then a good brush through. You transform the dog honestly.
Don't buy the other johnson talcs they are just that real lime talc. Not that great for dog skin or human.
Not an expert in dog skin but I read many sites and there are always great little tips. A lot of terriers that are double coats or wire coated tend to have a dryer type skin so there tends not to be a lot of oil to moisten the skin.
Enviromental infulences play a big part.
Weed killers, biological soap products, carpet and fabric mites such a creeping dandruff.