Thanks for all the replies.
My husband phoned a forest ranger yesterday who said no one had ever asked him about camping in a sno park before. The ranger suggested that it is probably OK if it isn't expressly forbidden. We're going to call another ranger district for a second opinion today. Some of my hesitation to camp without permission is not wanting to bother our kid if we get kicked out and have to move. Most of my hesitation is I would be unbearable grumpy if we got kicked out and had to move.
We've enjoyed our few nights at the Lake Alpine and Hope Valley sno parks in CA last year.