It gets plenty wet and plenty cold in Amsterdam. In fact, most days of the year there's a decent-or-better chance of rain. So, what we would do (I'm no longer in town) is:
1. Take thin "rain ponchos" for riding
2. Check out cloud radar website, like buienradar.nl , to decide when / via what route to bike
Also, there is absolutely no problem for the Dutch to bike at temperatures below the freezing point, in the height of winter (even though, granted, it isn't that far below zero centigrade). The bike paths are cleared of snow and things work just fine.
https://www.youtube.com/watch?v=Uhx-26GfCBU
Aptly titled "Why Canadians Can't Bike in the Winter (but Finnish people can)"