Just a thought here but I'm guessing that since the river doesn't freeze there has to a tremendous amount of water vapor, fog, mist, or what ever you want to call it rising up from the river. Obviously in the colder months what ever that lands on is going to freeze. I would move it as far away as you can from the river.
Sounds like your in a no win situation there. Don't own that type of station so I don't know if a heated rain gauge is available. As for the anemometer, whew, I don't know.
Maybe some of our members in colder climates have had issues like this and could chime in.