Assuming that the rules would be the same as when men's regionals were held at campus sites, it depends. Usually whoever was the home team got to use their regular dressing room. However, in 2002 with the regional at Yost Arena in Ann Arbor, George Gwozdecky and Craig Dahl threw a hissy fit and not only made Michigan use a visiting dressing room, they made them chip the Michigan logo out of center ice and and put in something neutral. So, the higher seed can force all of that if they really want to be complete *******es. Not that it did either St. Cloud State or DU any good.
That regional also featured the Michigan student section serenading Ron Mason off the ice after he lost the last game of his career to Colorado College and Mike Komisarek dropping the St. Cloud mascot with a cross-check before the game; the Husky had gotten up in the Michigan players' grill taunting them during the introductions and then made the mistake of skating right through the team as he was leaving the ice.