Countability, when it comes to infinite sets, should not be taken as its normal meaning.
A set is said to be countable if there exists a bijection between its elements and the set of natural numbers - that's all. No matter how unintuitive it might feel, if it meets this condition, the set is countable.
So hair on head is a countable set because there exists such a bijection. Same with set of natural numbers, set of positive rational numbers etc.