Coating charcoal around your eyes will help a little, but to be properly protected you need some special googles. While I don't know of any transparent natural material with UV protecting properties, the inuits (and probably others) made googles with slits in them, to reduce the amount of sunlight which hits the eye. Especially important it is to remove the reflection from the snowy ground.
If you of some reason has gotten snowblind, you need to stay indoors in the dark for a number of days days, the length depending on the severity of your case. You will know that you have been cured when it does no longer feel like needles stinging your eyes when you look outside.
Very soon I'll post instructions on how to make more advanced snow googles of wood. Not many photos I'm afraid, but hopefully the text alone will be suffcient.
Here is a photo of some quicky birch bark googles in usage. They work reasonably well, but the slits could have been made narrower.