Hey Andrea,
do you have any chance to workout inside? If yes, i would recommend you training at least the core and leg part of the workout inside your room/house whatever!
Like yam said, a good warm up is essential and even during the breaks you should do slight jumpes whatever do keep your body warm! :-)
you should not wear just one big jacket, try to wear more than one object, for example a shirt, sweatshirt, small jacket, big jacket :-) you can decide during the workout whether you want to wear anything or not.
in addition you should try to find some gloves :-) i found it personally very hard to even hold myself without gloves on a frozen and cold bar
I'd say: Go inside. Working out outside in the cold is not optimal.
Chris there are no gyms with bars unfortunately; last year I made a little calisthenic gym in my cellar but the height isn't sufficient for muscle ups; so now I buy a bar in my terrace and I want to train after luch , but in my city there isn't too much cold