To my knowledge there is no "Test Engineering" degree offered by any reputable 4 year college. In fact, I doubt that most test engineers went to college planning on being a test engineer. Of the many test engineers I've known, their degrees have been in EE, Physics, CS, and ME - that list is roughly in numerical order as well. Are college students aware of test engineering as a specific position? Probably not.
This is different if they are CS majors. In that case, they've probably been exposed to software testing theories in classes. There are scores of books, websites, and blogs on the subject. They may have even interned as a SQA (software quality assurance) engineer. I've met Microsoft testers, and they've said that most programmers hired start out in a testing position before they do anything else.
But I think hardware testing is a lot more dependent on exactly what you are testing, so the nature of it is harder to teach in a classroom setting. Yes, there are a few books that present an overview of the subjects (like Test Engineering: A Concise Guide to Cost-effective Design, Development and Manufacture by O'Connor), but it's just an overview. You'll get exposure to the basic tools (oscilloscope, DAQ cards, etc) in EE classes. You may learn about statistical methods in a stats class or industrial engineering class. But to really learn about the specifics of testing in a certain field, then you have to dig into the details. For example, you'll never learn about the details of fiber optic testing in an undergraduate class. You either learn that on the job or maybe from a book (like the excellent Fiber Optic Test and Measurement by Derickson).
Of course, what you major in during college is not necessarily a predictor of what you'll do in life. I once worked with a manager of the Integrity Program for the F-22 at Lockheed Martin in Ft. Worth, TX. It was a fairly prominent engineering position with a good deal of responsibility. He had a BA in philosophy....