The word "cold' is a mass noun, meaning that it's uncountable noun. We cannot count cold as we cannon count hot. Nevertheless, we find a usage of "to catch a cold" using of an article before the mass noun "cold".
What is the explanation for that?
It's not uncountable in the case where it's referring to the illness.
I caught a cold last week.
This winter I've had three colds.
The noun cold has two basic meanings :
cold noun (ILLNESS) Countable
a common infection, especially in the nose and throat, that often causes a cough, a slight fever, etc.
She caught a cold at school.
cold noun (LOW TEMPERATURE)Singular or Uncountable
cold weather or temperatures:
Don't stand out there in the cold, come in here and get warm. My feet were numb with cold.
Thus, in your example it is a countable noun.