Just to add a bit of science, I work for a company that sells moisture measurement equipment.

Even though whistles might be at room temperature, when blown through you are blowing a stream of warmed humid air. If you use metal whistles then there is more chance of a condensate forming as they are more likely to warm up quicker than a plastic one. The walls are thinner and metal is a better conductor of heat.

If the room is cooler than your breath and whistle then the condensate forms more rapidly. If the humidity in the room is higher then the air you breath and exhale is also carrying even more moisture.

I too am learning to play whistles and mine dribble! The humidity here in Shanghai is high as is the temperature so the air can carry much more moisture in a gaseous form.

As the temperatures and humidity drop I am just hoping I will dribble less!