It is an old wives tale that you get sick from being cold. But, if you are sick, staying warm is important, especially for your lungs. Also, if you don’t dress appropriately in general you are placing undue burden on your body to keep your temperature up. But, you are right in the most literal way, you catch the flu because the virus enters your body either by someone coughing or sneezing on you, or you touch something that has the virus on it and you touch your eyes, nose or mouth.