Yes exercising out in the cold is still safe as long as you bundle up and dress warmly enough for the cold weather.
I walk and jog all the time in cold weather and I've never had any problems and a lot of other people also exercise, walk, jog and run in cold weather.
But during really cold weather when you go out Jogging, Running or Walking don't stay out too long and be sure to go inside somewhere if possible or even your own house and warm up before going outside and exercising again.