Most often only the narrow "Shore"-parts of Frozen Oceans are called Frozen Deserts ingame. Larger types of Frozen Deserts can be found inland and normally consist of Dead Grass (on Dirt) covered with a thin layer of Snow. It's not uncommon for tiny valleys between Snow-covered Canyons to be called Frozen Deserts too.
On Shorelines you might find Sand under the Snow in Frozen Deserts, but more often Ice as the top layer over Ocean Water. Sometimes a layer of Ice might also be discovered between Dead Grass and Snow in larger Frozen Deserts, which perhaps indicates frozen rivers.
In frozen Canyon-valleys different types of Canyonstone like Canyon Floor or Dark Canyonstone can be found under the Snow. Only very rarely larger areas of Frozen Deserts will actually feature a significant amount of Sand below the Snow or under an additional layer of Ice.
In these biomes, Blizzard Chizzards will spawn during the day, and Arctic Mirus during the night, and occasionally some Night Chizzards too. During the night, Wood Treasure Chests are able to appear randomly in complete darkness too.