At first, I was thinking the same thing as Matt. But then I started wondering about how the ice forms over the water and some problems became apparent. Ice tends to grow from shore toward the middle, so it will reach out from your bank toward the wheel. The churning action around the wheel will prevent ice from forming on the water's surface, but it will adhere to the sides and buckets of the waterwheel. It will grow a rime over all of the surfaces that get splashed, making it heavier. I don't see weight as a problem on your humungous beam, but the pivot point will be more stressed now.
Putting anything into the water upstream of the wheel, like a dock or a pier, will slow the water down and could also offer another spot for ice to get a purchase and grow on the surface.
Does your river usually freeze over in the winter?