Can people naturally read body language or is this a skill you develop and hone over time?

I believe we all have it, but some choose to ignore all the signals until they see it in black and white, and so they then say it 'doesn't' exist.

It must be learned.

I believe that it works both ways.  I am like that.  I always have been, even since was a child.  I just knew what was right, or wrong, or when something was off, etc.  I carry that knowledge into my adult Life and it is also quite useful on the job so to speak.  You know that you know, but you don't quite know HOW you know. That's me. And yes, I ready body language quite well.  

A bit of both

Be aware that body-language is not universal. It varies from one culture to the next

It's a skill you learn.

I don't think it's possible to ethically design an experiment to test this for sure because it would involve raising babies with zero exposure to human body language.  As it is I'm not sure it's possible to separate from language acquisition and reading intonation.  Some features of body language appear to be universal but others are without doubt cultural, so they have to be learned by incomers.  Failure to pick up on any body language at all as a child is indicative of something wrong just like it would be to fail to pick up on language and intonation.  This is why language and communication therapists exist and they can do a lot to help a young child find a hook to start understanding.  It's also true that these things can always be improved on with study, it is, after all, what adults have to do when they encounter a new culture of communication.