You can't get sick from running in the cold.
However being out in the cold could increases your chances of getting pneumonia but the cold itself does not make you sick.
You could also get hypothermia from being out in the cold too long but you won't and can't get a cold or flu virus from running in the cold or being out in the cold.
Running in the cold does not make you sick.
However you may get pneumonia if you're out in the cold too long whether you're running or not.
If you do run in the cold make sure to bundle up good enough to stay warm and don't run for too long.
You cannot actually catch a cold or flu from being out in the cold as the cold and flu is caused by viruses.
However your immune system can be weakened some when your body is cold.
It can be harder sometimes to run in the cold and you could risk exhausting yourself out much sooner than you would when running in warmer weather.
But running in the cold weather is pretty healthy and will not make you sick unless you stay out in too cold of weather for too long then you risk frostbite or hypothermia if you don't wear gloves or protect your face.
You cannot catch the cold or flu from being out in the cold but it could increase your chances of catching Pneumonia so only run outside for a little while 30 to 40 minutes or less but no longer than an hour and always get back inside where it's warm and dress warmly for the cold weather and you should be fine.
I run a lot even in the cold weather but I dress warmly and don't stay out longer than 30 minutes at a time which is enough to give me some daily exercise so I stay fit and healthy but not long enough to cause me frostbite, hypothermia or any other harm.