Well it's currently an advisory. Unnecessary travel is not recommended, not outright banned.
Once it's an actual ban, if they pull you over and decide to ticket you it can be up to a $500 fine and a class B misdemeanor versus a lesser citation.
In terms what they will direct you to do will be mostly dependent on the situation where you are/road conditions.
In most cases these tickets will be issued once you actually become stuck. If it's bad they aren't going to be out driving around looking for people to pull over which would only create another dangerous situation.