Nope, all trails stay open, even ones in use at the moment of the race. They have a very good system for keeping both snowmobilers and sled teams from getting hurt. It's a really cool thing to see too.
We were up there last year on that same weekend, no problem. Just pay attention to what days and town they are going to run to and slow down around blind corners near those areas. The dogs like to take the inside line sometimes and it may be your lane. Just pull your sled over and watch the teams pass by, it's FUN to watch them.
Had a great weekend, rode briefly with the dogs Friday night. Hit some untracked groomed trails and introduced my 16yr old to one of the best places to be......gotta love the UP!