Is the continuous form of "have" ok in the sentence "he's having a cold"? Or is it ONLY correct and possible to say "He has a cold"? I can't figure out if in this case "have a cold" is a state verb or not. If it were, it couldn't have the continuous form.
Some verbs have two different meanings or senses. For one sense we cannot use a continuous tense. For the other sense we can use any tense.
In sense 1 there is no real action, no activity. This sense is called "stative". In sense 2 there is a kind of action, a kind of activity. This sense is called "dynamic"
to have: 1. I have a pound now. (Non-Continuous Verb: I possess a pound.)
I am having fun now. ( Normal Verb: I am experiencing fun now.)
I can’t answer the phone, I’m having a bath. (Normal Verb: I’m taking)
We will be having a party on Friday.
Therefore, the answer is: He has a cold.
Colds cannot be continuously had. You have to use the simple present to describe when someone currently has a cold, ie, "[Luke] has a cold."