A windmill is basically a inverse airplane - and airplane wings don’t like icing. I assume you could heat the blades but at some point you’re consuming more energy than you’re making.
I have to imagine it's really the overall weight or the unbalanced weight not being good for the bearings and such. Not to mention a blade flinging a piece of ice off when it starts to melt...
There’s also the issue of balance.
Thinking about it, that does make perfect sense, but just intuitively, I would think say, making a blade that had a flat side perpendicular to the wind direction would work, because the force can still be imparted to the blade. I can also intuitively surmise why that wouldn't work for a plane though.
When dealing with a plane, you want to generate force perpendicular to the wing (i.e. up when the plane is moving horizontally), but in a turbine you want the force to be in the same direction as the blade is moving. I feel like I must be missing something.
And of course old windmills were just boards - and I suspect they only stop working in the cold if the bearings freeze.