I love Europe in the winter (mainly for the winter sports, Christmas markets, and classical music seasons), but you have to plan different sorts of itineraries than you would in the warmer months. First of all, due to the greatly reduced hours of daylight (as little as 8 hours), you have far less time to explore the countryside. Especially in NW Europe, thick fog often further reduces your chances for sight-seeing. But, these restrictions apply far less in the cities, most of which are well illuminated.
Your question about ice and snow- you are most likely to encounter a significant amount of snow near the mountains in parts of Germany, Austria, northern Italy and Switzerland. Lasting snow cover in the other countries isn't too common. But, unless you find yourself caught in a particularly bad storm, snow removal in most of the areas where it commonly falls is VERY efficient. Barring a freak storm-of-the-decade, snow rarely disrupts transportation, especially trains, for more than a few hours. You can minimize potential delays by using public transport whenever possible.
Finally, adding to the other comments- your wish list is simply too long for 21 days, especially in the winter when you might hit transport delays. I would carefully plan and prioritize what you want to see in each destination, and research travel times at Viamichelin.com and the various national rail sites. The more ambitious your itinerary, the more you need to allow flexibility for the weather. You can plan around "most likely scenarios" for weather, but as the freakish blizzards of the past winter show, sometimes anything is possible. So, the watchword of planning a trip to Europe in the winter has to be this: Flexibility, flexibility, flexibility. That being said, I would still rather travel to Europe in January than July. I can always put more clothes on to stay warm, but you can only take off so much clothes when it gets oppressively hot.