Ah. That's the problem! You must be a Michigan Troll (lives below the bridge) rather than a Yooper (north of the bridge). Yoopers take their hockey much more seriously. [it is a Michigan joke folks]
Suggestion? Meter the ice at various points prior to the game. What you are looking for is the relative difference in lighting, not the actual exposure (unless you WANT gray ice!
). Set your camera on manual and select an exposure for the middle light level and keep one finger on your e-dial to shift your aperture up or down as you track the action. It will be a good test if you can walk and chew gum at the same time.
But seriously, even if you miss making a couple exposure adjustments, you may still salvage a useable shot adjusting the over/under exposure in post processing.
In Michigan Tech's ice arena - and I assume many NCAA Division I schools - strobes have been mounted above the ice and official photographers trigger them with RF triggers. Exposure is all pre-determined so all they need to worry about is focus and composition.