I'm so cold-natured that I don't hesitate to wear merino-wool long johns under my slacks in the winter, even if I know I'll spend much of the day indoors. YMMV.
I love 97% (approx.) nylon slacks for their ability to shed water. They are not waterproof, but they help prevent getting soaked to the skin. An underlayer is additional protection and will also help on windy days. I don't find the nylon slacks very windproof.
I don't generally take a full-length raincoat to Europe, because it's such a pain to carry it around on the days I change hotels; such a coat wouldn't fit inside my usual 24" suitcase. For a trip to just 4 Central European cities in March (i.e., three hotel changes), I'd seriously consider dealing with a long raincoat rather than taking just my usual rain jacket. Cold weather is a lot more miserable if you're also wet.
I'd want something to cover my ears--at least an earband of some sort if opting for a baseball cap instead of a more typical winter hat.
I'm not as anti-umbrella as many others. You do have to be careful not to hit other people, but the sidewalks will not be as crowded in March as they are during warmer months.