Do you think most videographers and film makers have a degree in the field or are most of them self-taught? I don't have a degree, but I am good at learning by myself. Do you think that could be a problem when you want to apply for a full-time job?
The industry is more focused on skills, so I don't think a degree would be that important. But, the market is tough if you're looking into applying to companies. A degree might be needed, in that case, depending on the qualifications they want.
I guess some companies are still "old-school" in that sense and they, will probably ask for a degree. It's hard to change the habits of the corporate world. But if you are a freelancer, you definitely don't need a degree!
Certificates may suffice now with the multiple online courses available. Obtaining these might help if you're going to go freelance and make a name for yourself. Even practicing your skills might do you better than having a degree since the field is more skill-based.
I haven't met a client yet who asked where I went to college. (I didn't) This is one of those businesses where the work done speaks to the experience of the photographer, and speaks directly to the customer.