Being born and raised in Lake Geneva, I can personally say stay off LG.... LG is one of the most dangerous lakes in the state because of springs and west to east rapid water flow under the ice...... God bless the family, hate to hear of this.
I didn't realize lake geneva was that scketchy. Only time I was ever on it I got invited to ride ice bikes with a BSA dirt bike club. They used to plow a track right on Williams bay with a truck( not sure if they still do?). The only reason I bring it up is because the year I went up was not a great winter. I remember being surprised how much ice was in the bay even though the chain-o-lakes in IL was wide open.