"I have got a cold"/"I've got a cold" isn't really present perfect. It's present perfect in form, but in meaning, it's present: I've got a cold has the same meaning as I have a cold. And it also depends what variety of English are you speaking. People also tend to say: ''I got a cold''...it normally means "at one point in the past, I caught a cold"
...but is often used colloquially to mean "I've got a cold". ;-)