Hi, I'm not familiar with the current crop of White Mountains. In the old days, you had to add ice and salt to the WM to provide the cold.
I have a Cuisinart with a freezable container. Cleaner, neater and easier to use. I'm very happy with the ice cream I can make in it. The downside is you have to freeze the container overnight before churning. But, you should make the mixture the day before as well.
"If you want to make an apple pie from scratch, you must first create the universe." -Carl Sagan