Since "hair" in English can be countable or uncountable, could this be translated as "How much white hair"?
Hair is countable in German. So, it would be how many white hairs due to context.
Now if you would say "Er hat weißen Haare" that would be "He has white hair."
You are correct that we count hairs in German but not in English, but you got the adjective ending wrong: "He has white hair" = Er hat weiße Haare.
To the other commenters: Yes, this is an example where you can't translate the plural literally between languages without making it sound weird. This is one of those times when you have to modify things slightly when translating.
It could be both:
"Wie viele weiße Haare sind hier ?" => nominative "Wie viele weiße Haare hast du ?" => accusative
My question was a little different to what's below. Is the attributive adjective 'weiße' in this instance because it's accusative plural (Die Haare) thus adding an 'e' to 'weiß'? Sorry, just struggling about with attributive adjectives, as far as I can see this is neither the definite nor indefinite article (plural discounts indefinite anyway).
Exactly. There's no article and the case is either nominative or accusative - we can't tell, but in this example it doesn't matter as the result is the same for both.