Frost flowers often grow on new sea ice. They are thought to have a high specific surface area (SSA) that provides sites for heterogeneous reactions. We have measured the SSA of frost flowers using CH4 adsorption at 77 K and obtained a value of 185 (+80 -50) cm2/g, much lower than inferred by others. Their density is 0.02 g/cm3. We calculate that the total surface area of frost flowers is 1.4 m2 per m2 of ice surface, so that they do not increase the ice surface area significantly. Their role as sites for enhanced heterogeneous reactions should be reconsidered. Frost flowers also commonly grow on fresh water and the saline brine seen on young sea ice is not necessary for their growth. Photo- and electro-micrographs reveal hollow and concave structures, typical of very fast growing crystals. The brine that wicks up frost flowers considerably perturbs their growth.