Heat isn't the only issue. From Wikipedia for the Netherlands:
Ice days (maximum temperature below 0 °C (32 °F)) usually occur from December until February, with the occasional rare ice day prior to or after that period. Freezing days (minimum temperature below 0 °C (32 °F)) occur much more often, usually ranging from mid-November to late March, but not rarely measured as early as mid-October and as late as mid-May.
I live in Montreal. I bike 9/12 months, and just take public transit / car sharing services in the winter months, or when I need it. I assume the Dutch do the same. I also lived in Austin for 6 months until July, and I found that the weather was pretty uniformly bikable because the heat was dry, though yeah, having showers at the office can be necessary if you live far away. It almost never rained, though. That's a big plus for biking.
Like most lifestyle issues, it's mostly just a matter of getting used to it.
From my perspective, the worst months in Austin (July and August) could be doable with a shower at work. Without one--totally unthinkable unless your job involves outdoor labor. I biked daily for 3 years when I lived in Boston but there's just no equivalent to putting on a big jacket for heat/sweat.
Look at the dew point (which far better comparison than humidity because it doesn't fluctuate with temperature). Here are the August daily averages for Austin[0] and Toronto[1].
Toronto's dew point range (~53-63) has a max that is right around our minimum (Austin range: ~63 - 72).
Also keep in mind that, Toronto's daily high temps in August (~77F) are right around Austin's lows (~76), with our highs reaching around ~97F.
I'm going to suggest that you may be misremembering how humid it felt - in my opinion there's no way to bike any reasonable distance for the majority of July and August (and often June and September as well) without showing up a sweaty mess. At least I haven't figured out how to do it--even though I bike commute regularly from October - May.
Bike paths and roads are diligently cleared/salted in the Netherlands. So many people rely on bike paths to get to work or their train that I doubt ride sharing or taxis could handle the load.
The train is a big deal. Judging from comments I've read on web forums (granted, a pretty noisy and biased data source), most Dutch with longer commutes will combine cycling and public transit. In contrast, an American with a (say) 10 mile commute, must choose between cycling and driving. Those who do commute by bike in the US are dealing with more extreme weather and longer average distances, with little or no bike infrastructure.
If everyone cycling in the netherlands would take public transport or drive when it's cold/snows/rains the roads would be in constant gridlock and public transit would collapse.
During the winter, I ride a bike with studded tires. It makes a huge difference -- even black ice is navigable with care. Knobbly ice is actually worse because it pushes the bike around.
I live in Madison WI, and was curious about how it compares to Amsterdam for weather: About 15F hotter and 15F colder, give or take, also with more day-to-day variation.
Winter cycling is definitely its own beast -- not just weather but also darkness and the attack of road salt on the bike. I've got a dedicated winter bike that comes out when the salt trucks come out.
Much as I love riding throughout the year, I don't even mention it when I'm encouraging people to commute by bike. For anybody who's on the fence, getting them to try riding once per week during good weather is a great start.
Ice days (maximum temperature below 0 °C (32 °F)) usually occur from December until February, with the occasional rare ice day prior to or after that period. Freezing days (minimum temperature below 0 °C (32 °F)) occur much more often, usually ranging from mid-November to late March, but not rarely measured as early as mid-October and as late as mid-May.
I live in Montreal. I bike 9/12 months, and just take public transit / car sharing services in the winter months, or when I need it. I assume the Dutch do the same. I also lived in Austin for 6 months until July, and I found that the weather was pretty uniformly bikable because the heat was dry, though yeah, having showers at the office can be necessary if you live far away. It almost never rained, though. That's a big plus for biking.
Like most lifestyle issues, it's mostly just a matter of getting used to it.