Air is not saturated at high altitudes! Why it should be? First there is very little moisture up there. When air ascends it gets saturated, clouds form, rain starts water drops back to the ground so you have dry air at the altitude. Second to get air saturated and fog or cloud to form you need temperature to reach dew point. Not to many people know but when air ascends not only pressure drops but dew point also drops! This has something to do with water molecules being far apart. So at altitude you have very dry air with very low dew point. But if it gets saturated sometimes very small ice crystals will form. That's cirrus clouds. But they are not thick for the reasons stated above as there is no much water left.
It's dangerous to use anti ice in these conditions because you will can melt ice crystals but water can freeze instantly as it is very cold outside and you will get clear ice icing down the wing which will be dangerous.