There was some interesting research that was done, i'll share it with you:
Our bodies have the ability to divert blood to areas that need more of it. For example, when you study more blood is sent to your brain, when you eat, more blood to your stomach and the most known, when you exercise more blood to your muscles.
Our blood contains white blood cells which are the bodies soilders which fight infections. Our bodies, at normal temprature divert quiet a bit of blood to our noses, thus directing a lot of white blood cells to our nose to help fight any infections which we might breath in.
When we are cold, our bodies divert blood away from our extremities and towards our core and vital organs to keep them safe from the cold. This is why your hands, feet and nose get cold first as our bodies divert less blood to these and more to our core. Thus, when we are cold less blood is directed to our noses, therefore, less white blood cells to fight off any infections. Thus, why we may get sick. But the cold is not necessarily the direct cause of such sickness.
So, it seems like our moms are right, put on a sweater or you might catch a cold! :)