What would the Earth be like if the core was water rather then magma?

Very cold and of low mass. There would be less gravity because the mass of water is lower than the mass of magma, and like much larger than it is now. There would be no surface or crust because there is nothing to support it. There would be no heat convecting up from below to keep the earth warmer. Come to think of it, we could just be one big ice ball.