As someone not currently working in the industry (just practicing it on the side for my own uses) I would tend to say that your actual degree is not that important. What's more important is your skill set and, most importantly, your portfolio of works you've completed to show you actually have the drive and skills to make something useful.
All the skills and degrees in the world are useless if you can't show that you know how to implement them correctly. And in general for coding there is a high proportion of people working in the industry who majored (in college) in a different or unrelated field.
A computer science degree might help but isn't necessary. In fact there are plenty of arguments against a college degree in computer science:
*It will cost you thousands of dollars whereas self-education (books and practice) cost only hundreds
*You may be required to allot time to learning skills that might not be useful to you and take time from working on the stuff that you do like or are interested in.
Again I'm not the most hardcore coder but this is generally what I have gathered from my experiences. If a more experienced coder feels like jumping in I hope they do just that.