Well, plus sugar. And air. But to a large extent that’s pretty much true. The bulk of an ice cream matrix is ice crystals and reduced cream, with lots of little air bubbles mixed in. The amount of air depends on how much churning you do, but then I’m getting ahead of myself.
The first ice creams were actually sweet shaved ices (or snow) with a little cream added on for extra richness. The trouble with simply combining cream and shaved ice, though, is that the cream always stays liquid (since its freezing point is so much lower). The reason has to do with fat. All those little blobs get in the way of the water molecules as they try to get together and form crystals. Add dissolved sugar and there’s even more debris in the way, and so the freezing point goes still lower. Yet when the temperature gets low enough ice crystals do manage to form in the cream. Robbed of its moisture (since ice can only form from pure water) the cream reduces, becoming a super-rich, super-thick, and super-sweet flowing liquid held in place amid ice crystals. This is what accounts for ice cream’s semi-solid consistency.
Yet air plays a significant role in ice cream, specifically tiny air bubbles which, like the fat and sugar, keep the ice crystals from forming large, continuous masses and turning the whole matrix rock-hard. Thus mixing or churning the ice cream as it sets up helps keep it soft and scoopable. More on that very soon.