As far as the cold... as long as you're dressed appropriately it shouldn't be an issue.
What scared me away was the Yankee's seat previewer. You can see what your view would look like form your seat online, and the majority of the view's I saw from seats I could get were so low to the ground you wouldn't be able to see anything.
This game seems like a great headline for the NHL... a game from world famous Yankee Stadium, but as far as I'm concerned the fan's are just a prop for TV.
I almost wish the Devils got it in 2015 so they could play it in Met Life Stadium. There is much more upper deck there where sight lines would be good (still far away, but at least you can see the entire sheet of ice.