This answer is only addressing one aspect relating to skin and coat color.
Skin cancer and sunburn
Lighter colored skin is more prone to sunburn and skin cancer. Generally there is a link with coat color and skin color. White hair, fair skin, black hair darker skin. However, some breeds are more susceptible to skin cancer, irregardless of color.
Melanin is the natural pigment that colors the skin. The more melanin the darker the skin. Like in human beings, melanin protects the skin cells from the sun's UV rays.
The dogs most at risk of skin cancer:
Light-colored dogs with thin haircoats that spend time in the sun have
a higher risk of developing certain forms of skin cancer. Some
breeds of dogs (boxers, Scottish terriers, bull mastiffs, basset
hounds, weimaraners, Kerry blue terriers and Norwegian elkhounds) have
been found to have a higher incidence of skin cancer thereby raising
the distinct possibility of a genetic link. Male dogs who have not
been neutered have a higher incidence of perianal tumors. Generally,
the age of a dog also plays a role as middle age to older dogs are
more likely to develop cancerous growths