Engineers are always problem solvers, no matter the field.
Any career you have will be solving thorny problems were there seems to be no clear good answer (if there was, they wouldn't need you).
Careers that relate in the field are solving problems ahead of the design, like pitching your product so that the customer (usually government) will buy it, or solving problems after the design, like scheduling and delivery of the product.
Aerospace engineering has always been about math, physics and systems engineering, and has always been a small niche, but if you are willing to adapt and always seek to solve the biggest problem your company has on the table at the moment, you will do fine and have many career options.
College will teach you math and physics, which is about 25% of what you will need to know to succeed. Then you have to learn about managing people, systems, economic and maintenance concerns, and always look to slay the biggest problem on the table.
Virginia Tech '00