It can snow and be cold or it can be wet, gray and not so cold. Winter in Germany is not a constant thing. In general winter is mild and rainy. Only in higher areas you have real chance of snow. So driving conditions won't be perfect but not bad either. Make sure the car you rent has snow/winter tires or at least all-season tires on it. If you decide to drive into mountain regions (there are none around Hamburg) but still if you want to do that make sure to have snow chains with you since sometimes snow chains are mandatory on certain roads.