Not necessarily. Cold causes vasoconstriction and that hardly causes to increase the blood flow if not to reduce it. The major effect of cold/ice application in such cases where there is some "swelling" due to any type of inflammation (aseptic or septic) is to reduce the local blood flow through vasoconstriction and as a result, reduce the inflammatory agents that are released from the blood vessels/capillaries into the intercellular medium. Removal of lactic acid has very little to do with the "swelling" issue. In short, cold application and elevation of the lower extremities can help to recover from hurtful feet after dancing.
Icing is very effective and therapeutic. The body increases circulation to the iced area. The increased blood flow reduces swelling and clears out lactic acid and other irritating substances. Ice is a "wonder drug".