Well the snow might be a good thing to give your arm a rest!
For walking on ice, you might look at something like this. Ben has these and the really work wonders!
They are slip on chains that have metal blade like cleats! They are easy on and easy off.
He uses them all the time on the frozen lake and can go right along! :-)
Wow, those are are really nice! In general I would say they might be a bit of over-kill for around here, considering the fact that there is usually only a week or two of below freezing weather. Sometimes it won't really snow in a season. The next few days look cold and snowy though so I could use a pair this season.