Being a car designer is certainly attainable, but it does require a specialized education, and it also is incredibly competitive.
I use the analogy often that if you want to be a car designer, you need to be as ready to design the cupholders in a minivan, or the hubcap on a pickup truck as you do the super sleek sports cars which you see everyone drawing in their portfolios. If you look at sites like Cardesignnews.com you can see their portfolio section is spilling over with incredibly hot sketches, fantastic 3D models, and most of those people are still unemployed.
I too dreamed of being a car designer, and after having been given the chance to briefly work on a co-op project with General Motors (Pre bankruptcy) I realized that the car design world is super focused, highly constrained by existing norms and designs, and innovation or outside the box thinking is rarely promoted. Most of the awesome concept cars you see at the car show this year will be stuck into a storage locker never to be seen again by next year.
That’s not to say you couldn’t apply a transportation degree elsewhere. Transportation designers can work on anything from airplane interiors, to train locomotives, to boats. The skillsets focus on being able to understand very complex form and aesthetics, and communicate those ideas through highly emotional sketches and renderings which help “Sell” an idea. This is why every “hot” sketch you see posted on Autoblog always looks quite different once it becomes an actual vehicle. The designers will help the process along the way, but the auto industry is still very segmented. IE a professional sculptor is in charge of actually building the clay models you see, another person converting it to 3D, all overseen by a design manager/lead designer who controls the vision which you contribute to.
The pay often isn’t as good as it should be either, at least here in the states. Jr designers in the US will either be working in California or Detroit, and since the field is so competitive unless you are the best of the best, the salary doesn’t need to be as high. I have known 4 car designers and all of them left the auto industry to move into video game art (modelling cars in 3D for games), bike design, movie prop design, or consumer products. So the skill sets can transfer over to other fields as long as you don’t let the rest of your brain atrophy in pursuit of the hot sketches.
My views certainly don’t represent everyone’s opinion, but there are some pretty big issues to consider if you want to focus specifically on cars. The main transportation programs are also all at private schools, so you can expect very high costs for tuition.