Sounds like you want to go into the TV/Film Industry. Any college's school of communications or film school would work the best for you. Some majors that you can look into are Audiovisual Communications, Cinematography and Film, Communications Technology, or any other major that has to do with television, film, or communications.
Video editing is a constantly growing industry to go into, and it proves to be very rewarding. Editors make a healthy amount of money, whether they are freshening up a video or editing an entire piece together. I think it's a great industry to go into, so you should definitely apply to one of the above majors and see for yourself!
I work with a number of video editors at my jump, so I looked into their backgrounds. In addition to what's already been posted, I'd add computer graphics, digital film making, TV production and communications.
I think many will point out the obvious answer which is that a degree in film or media would be beneficial. While that is certainly true, the skills needed to edit videos are relatively easy to come by. A few dozen hours on YouTube and a handful of practice videos can make you relatively proficient with the tools.
I think what might be more valuable would instead be to educate yourself on how to tell a good story. Take course in journalism, storytelling and writing and develop a strong understanding of what makes a story compelling. When you know that you can add the nuts and bolts of video editing and be a much better content creator than someone who is an expert at creating videos but doesn't have anything valuable to say.
If you want to stay in the visual field, consider something like photography. It will teach you the fundamentals for lighting and composition but will also greatly enhance your "eye" when you're out on location. Cinematography is dramatically underrated by the general public, but it's those people with the eye for compelling shots that tend to win awards.