I am a Athletic Training Student as well as a EMT and last year i covered my school's D1 Hockey team. I had to spine board a athlete at RIT last year on the ice as well. If you are covering a game that is high school and above, there should be a AT there, College and above will have multiple AT's and team docs. The AT's and Docs handle basically anything that happens on and off the ice regarding the players. However, if a trauma or C-spine injury were to occur thats when you would need to enter the playing surface. beginning of the periods the ice is slick, but gains traction as it progresses. As long as you are deliberate with you footing, walking on the ice isn't hard to accomplish, just do not rush yourself. As far as spine boarding, have extra hands to help prevent the board from sliding with the athlete. If you need to reposition the athlete, have a ref or player put their skate next to the board to use as a brake. As far as walking with the spine board, bring the stretcher out with you, and just roll it off.
If you have any more hockey related questions feel free to shoot me a pm