The cold weather doesn't actually make people sick it's just that during cold weather people are cooped up around other people more often especially indoors during the winter months and that gives the virus more of a chance to spread from person to person.
The cold and flu virus can spread during spring and summer months as well though because I've gotten the flu and a cold virus during spring and summer before.
To get a cold and flu you have to get infected with the virus so the cold weather cannot make someone sick although it can bring on Pneumonia and hypothermia but you can't catch a cold or flu by being outside in the cold weather unless you're around someone else ho has the cold or flu.