The Whiteout level is unlocked by first collecting 20 Orologions (little stopwatches). These are pickups that drop from light sources. Once you have gotten 20 Orologions to unlock EXTRA: Whiteout you will unlock the new map ''Whiteout'' too.
If you have played before just load a level and quit out as it will unlock retroactively.
Once on the level you will need to head immediately south, the Antidote will be in the cave 5 tiles south of the start. The room has several enemies in it so just clear those before collecting.
If you have the Milky Way map it will show the exact location with an arrow.
Visual Guide: