Once again, your grandma was right (you eat your vegetables, right?). She might just have said "it's cold outside, you'll catch a cold" while the recent study published in the Proceedings of the National Academy of Sciences phrases it a bit differently ("Temperature-dependent innate defense against the common cold virus limits viral replication at warm temperature in mouse airway cells"), but the general idea is the same.
Rhinovirus, which is the most frequent cause of the common cold and "asthma exacerbations", can reproduce better at the lower temperatures found in a nose cavity compared to the warmer temperature found in lungs. It appears that this is because the body's immune system is less effective at cooler temperatures, thus giving the virus more leeway to get a toehold and, eventually, overrun our system.
This could partly explain why the common cold is so much more, well, common during the winter months. This is of course combined with other factors, including the fact that we have all those holidays where we meet more people than we usually would, shake hands, give hugs and kisses, and then all put out hands on the same doorknobs, etc. We also get less sun exposure during the winter, which reduces our vitamin D intake, something that is thought to also reduce the effectiveness of our immune system.
Jonathan Ball, a professor of virology the University of Nottingham, said the findings could explain why rhinoviruses infect the nose rather than warmer parts of the body like the lungs. "This could explain why the rhinovirus causes colds and is less able to cause more serious lung infections, like influenza does," he told the BBC.