Is it possible to travel to Europe for a week especially during winter with only a carry-on? YES! Here is my suitcase packed for one week — in January — and it is only a carry-on. Proof that it can be done!
I did carry a larger purse so I could hold random stuff on the plane at my seat (reading material, etc) and since it was winter I did bring boots, but wore them on the plane so I didn’t have to pack them. The key is to pack things you can layer and mix and match! I hate going somewhere and then when I unpack find a bunch of stuff I never wore, so I minimize as much as possible.