Sounds funny, doesnt it? You think that anyone that said that wouldnt know what they are talking about. Most wouldnt, I do. So, what do I mean by that? Dont move around on the board if its frozen? Simple, dont move around.
Reason being is that if you are on a fresh water lake or river and it is cold enough to snow or is zero on the temperature scale then you should consider against any sudden actions or movements because of ice. Yup! Ice! It can happen very quickly and catch one of guard easily. Even a subtle movement can cause your foot to slip and put you in a precarious position.
I will give you a great example: I was paddling while it was snowing the other and I was getting ready to do a buoy turn and as I stood back on my board my rear foot slid and almost came off the back of the board! Fortunately, I was able to keep my balance and not go in the drink! It did make my heart skip a beat but knew I was ok, I had my drysuit on so that gave me the comfort I needed.
Morale of the story: If your paddling in cold weather were ice is forming, be careful, like real careful!
Now get out there and go paddle! Winter be damed! ps dress appropriately!