If you mean, "is there a risk of catching a "cold" or the flu?", then...no. A "cold" or the flu are viruses, and can only be transmitted from "catching" the virus from someone else...transferring the virus from someone who has it to you, either directly or indirectly.
One obvious risk from going outside in freezing temperatures with wet hair is that your hair holds water...moisture...that keeps it pliable. When wet hair is exposed to freezing temperatures, it expands. If your hair freezes, it becomes less pliable and is certainly more vulnerable to breakage. So beyond the obvious discomfort, it’s definitely not a good idea to go out with a wet head in below-freezing temperatures.
Another risk is hypothermia. Cold air blowing across wet skin (scalp) can more rapidly chill the body, leading to hypothermia (body temp below 95 degrees).
When exposed to cold temperatures, your body begins to lose heat faster than it can be produced. Prolonged exposure to cold will eventually use up your body’s stored energy. The result is hypothermia, or abnormally low body temperature. Body temperature that is too low affects the brain, making the victim unable to think clearly or move well. This makes hypothermia particularly dangerous because a person may not know it is happening and won’t be able to do anything about it.
Hypothermia is most likely at very cold temperatures, but it can occur even at cool temperatures (above 40°F) if a person becomes chilled from rain, sweat, or submersion in cold water.
So, short term exposure of your wet head to cold temperatures can freeze your hair and leave it more susceptible to breakage, and long-term exposure can rapidly chill you...and possibly be very dangerous.
STAY WARM AND DRY!!!