Being cold or being out in the cold weather doesn't make you sick with the cold or flu but you can develop pneumonia from being out in the cold weather or being in a cold house with not much heat or any heat at all.
You can then get hypothermia which can make you sick and weaken your bodies immune system.
But the cold weather or cold temperatures are not actually the direct cause of the cold or flu because to get the cold or flu you have to actually get infected with the cold or flu virus.
The cold and flu virus is more active though in the cold weather but you can also get the cold or flu in the spring or summer.
I've gotten a flu when it was spring and even in the summer.
Washing your hands constantly and drinking plenty of water, orange juice, eating oranges and upping your intake of Vitamin C and getting the flu shot before the flu can help prevent you from getting sick with the flu.
If you have the cold or flu you should stay home from work especially if you work in an office where you can make other people sick or might catch another strain of the flu or cold virus from them.