How warm should I dress??!

I wear wool socks and waterproof hiking shoes, pants, base layer, fleece, rain jacket, hat, and gloves. It works for me in almost any winter weather.

I think it depends on how easily you get cold. I personally get cold very easily and would require warmer clothes than someone who lives in a cold weather climate would. I travel with a lightweight down jacket that stuffs into a bag. I can layer a rain jacket over it when necessary. You will want to keep your feet warm and dry, so waterproof shoes and wool socks would be ideal.

For chilly weather, a warm hat is essential and it should entirely cover the ears. Being water-resistant is a plus (and for footwear too.)

It really depends what your activities are. If you're planning on hiking or a full day walking outside, cold weather socks and waterproof shoes are a must (waterproof shoes area good idea anytime in Germany). Late March can be beautiful or it can still be winter.

That said, if you're not hiking or spending the whole day outside, normal winter wear will be fine, keep in mind drizzle to rain is always likely and that is probably going to be the thing that affects your more than cold, so waterproof shoes and a shell layer are needed.

Best is to check the weather forecast shortly before your journey. It can be everything from -10c to +20c especially in the southwest corner of Germany. More altitude makes it colder, appr. half degree per 100 m. Most important are the wind conditions. With south and west wind it can be really warm. East and Northeast winds can cool down the country significantly.

Info: the weather forecast beyond 4 days is very vague in Germany, especially in spring and autumn.

Normally you will find stores for clothes in every town or city, also with brands for cheap clothing.

Based on my very limited experience with cold and snow, here's what worked for me.

Feet - thin socks, then thick wool socks and water resistant footwear. Thermal undies are great if you are going to be outside for the day. Indoors - restaurants, museums, etc. - you need layers you can take off and put on easily, so thermals can be a problem. When it snows, a rain poncho will keep you dry - otherwise the snow will melt and if your outerwear isn't water resistant . . . Keep all extremities warm (that's where you lose the most body heat) - hands (good gloves), head (warm hat and scarf), as well as feet. You may want to bring a few foot warmers like these. I've used their handwarmers for several years.

If you are talking about a puffy or polarfleece vest and a waterproof jacket then that would work for me but I am pretty cold tolerant.

It's 32F and I just shoveled 3 inches of snow wearing a Lands End Heat Crew long underwear shirt (I size up and wear this for a regular shirt all winter) topped with a DriFit long sleeve quarter zip shirt and a puffy vest from Costco. Warm hat (a fleece beanie will work fine), fleece neck gaiter, glove liners. If it had been snowing heavily I would have worn my waterproof rain jacket over this combo to keep me dry.

I traveled to Paris, Belgium and Netherlands at the end of March thru mid-April. I encountered a lot of wind at times so the jacket was a good defense against that.

If you are a Costco member take a look at the Kirkland brand wool socks. They are inexpensive but very nice. For me they last about 2 winters then I go thru the heels. Since they are only about $4 a pair this seems like a good deal to me. I also love the Costco puffy vest. It's changed a bit this year but still inexpensive.

As MarkK notes, there are stores everywhere and they will probably have items more attuned to the weather in their area than stores in Los Angeles. Plan to add items as needed rather than carrying "in case" clothing.

Just returned from the xmas markets, and my toes never got cold, and I'm attributing that to wool/cashmere socks with my winter boots that had about a 3/4 inch platform bottom. I think this insulated me from the ground cold.

I've been in Europe March/April, and I've that found shoulder-season weather alternates between spring and winter, depending on the day. I brought a packable down jacket, packable FULL-LENGTH raincoat [or poncho would do], and layers.

Have a great trip!