Frost and snow, ice cubes in a drink and the ice that covers a lake are all the same material, though they look different. Impurities aside, water is water and ice is ice. Snow and frost form as intricate crystals whereas ice that forms on a lake or a puddle is more of a hard blob of water. The difference is in the formation. Snow and frost are formed directly from water vapor in the air. As tiny particles of water vapor adhere to the developing structure, they take on a crystalline structure.
When ice forms on a lake or in a puddle, it also has a crystalline structure. Break a piece of ice and see how sharp the edges are. It's just that these large blobs of ice are less rigidly organized. Of course, it is the shape of snow that causes it to accumulate with so much air in between the crystals. Fresh snow accumulation is about 80% to 95% air.