At low temperatures protein solubility is a little bit lower. More important, al low temperatures protein denaturation is also lower. This is a old method used for plant homogenates. It is not very good for animal extracts.
Cold Acetone is used because dissolution of acetone in water is an exothermic reaction. Moreover addition of acetone in water results in depression of freezing point of water. As a result in chilled acetone : water, the proteins not only precipitate in better way but their activity and structure is also retained.
You may possibly want to check: A. Alam, "Agent for protein precipitation, a method of protein precipitation, a method of protein assay using protein precipitation agent, and a kit for protein assay", US Pat. 6,875,617 B2; Apr. 5, 2005.