I am also planning a trip to Amsterdam, except in May (tulips!!!), and what I've discovered as far as tips, I'll try to put here:
-for a short trip, the I amsterdam card could be good, but we're planning to get the Museumkaart and go to museums all over the Netherlands while we're there for about 11 days:
http://www.amsterdam.info/museums/museumkaart/-I wouldn't be deterred by it being 'winter' in Europe, because I'm used to winter being -30 temps with tons of snow (Minnesota) so even a 20 degree day will likely feel like a heat wave to me after experiencing that
-I haven't traveled in Europe in the winter, but I'd probably just wear what I wear at home (in Minnesota) which is layers, layers, layers--I'm guessing a fleece jacket and a down jacket would be best to stay warm, just as they are in the US
-bring a book (or find an English bookstore) or crossword puzzles or other games and just hang out in parks/cafes and read/play/people watch - this is always my favorite thing when traveling - last July, we brought Quiddler
http://www.setgame.com/quiddler along on our trip and played in the airport, in the shadow of the Eiffel tower, etc. and we did a puzzle when staying with friends in Germany; drinking German wine and doing a puzzle in the dark evenings was surprisingly fun
-visit 'normal' places, because they will likely be very different... going grocery shopping, a visit to the library, etc. are interesting when it's not at 'home'
-on the advice of a Mustachian, we got the BarclayCard Arrival MasterCard and it's saved us $800+ this year alone (incl. sign up bonus which was equivalent to $400):
https://www.barclaycardus.com/-My preference is to stay in one place long enough to feel like I really belong there (usually 5 days), which is why we're going back to Amsterdam and want to explore other towns in the Netherlands, but if you like to spend time in the car or on trains, Germany, Belgium, France, and even Denmark are fairly close... staying in the Euro-zone might be easier in terms of converting funds, but if you've got the time, explore further - there are also fairly cheap flights within Europe (I think RyanAir and others I can't think of, just google around)
-if driving to other cities, keep in mind that parking costs (and gas) are kind of insanely expensive depending on where you go - our friends in Germany drove us around, and I know it wasn't cheap (they never let us pay so I don't know exactly how much... ahh, Germany hospitality)
-We used AirBnB and we likely will again - my only caveat is to look for the things that are important to you (for me, it's a comfy bed and proximity to at least a couple major sights) and read the reviews for mention of those things - small beds seem common in the European listings, as do hot plates vs. actual stoves - look for 'rooms' vs. whole apartments/houses if you want to pay less