It's not dangerous to run in cold weather as long as you dress warmly and do not over exert yourself.
When running in cold weather it can strain your body more and you will usually have a harder time breathing when you do run in cold weather.
When running in cold weather make sure you take it easy and if you feel tired then slow down and stop and rest for awhile.
Also wear a scarf and cover your mouth to help keep the air in your lungs warm.
I go running and jogging sometimes in the cold weather as long as it's not below freezing and I've been okay.
I just stop running before I get too tired and will sit down or lean against a tree until I catch my breath again.
Then after a 10 or 20 minute break I start running or jogging back to my house.
I would avoid running or jogging in cold weather if the weather is extremely cold such as below 32 F or in minus degree temperatures.