The difference is Mystique won't actually die if she stays in her blue form, and that's why that metaphor doesn't really work. Freeze needs his suit to survive. Ideals have nothing to do with this, it's about biology. It's more like someone who's immuno-compromised having to remain in a sterilized environment. If Freeze wants to live around people, he needs his suit. If he wants to take off his suit, he needs to be in a cold environment. There's really nothing else to it unless a cure for his condition were developed.
And the thing is because he's frozen over the city no one's going to be outside for him to hang around with, since they'll be trying to stay warm. He's still going to be the only person in a frozen city.