Hey, congratulations on getting to go to a hockey game!
Coincidentally
my team actually got to drop the puck a week ago at a hockey game, so we have a bit of experience with this as well.
Firstly I agree with everyone in this thread, mecanum definitely won't suit the surface. We used traction wheels and retained most of our speed and turning ability, both on used surface and new.
Secondly, you might want to tether the robot (if you have a long enough cord). We tested the robot an hour before and everything was fine, but five minutes before we went on suddenly our testing showed that some drive signals weren't transferring properly. We still could drive, but it was a bit hit or miss due to a few motors constantly driving. If you can bring it to test off ice during another hockey game, you can determine if that will be an issue.
And be careful about what you put on the ice. We were warned that we had to keep moving the robot every 30~ seconds while on ice to avoid melting small spots, plus any studs that are put in the tires will leave divots. Honestly as long as you have grip on your wheels, you'll retain most of your driving ability.
If you can, try to see if a local team will let you share their ice to test the robot before the match, just to give your drivers some practice. You can do some really fun spins and maneuvers on ice. Good luck!