I don't know where the notion of Odin ever wearing a mask came from. A simple Google search showed exactly the same two sentences repeatedly constantly at New Age and Wicca sites, especially jewelry shops selling "Odin's Mask" pendants.
"Mythology relates that Odin sometimes wore a mask when encountering potential opponents. This mask was so terrifying that enemies often retreated without any need for fighting on Odin's part, thus saving "AllFather's" energy, for more enjoyable and profitable pursuits."
None of these sites ever quote their sources, and a check of the hard resources in the Eddas and sagas showed no evidence of Odin wearing a mask for any reason. I believe this to be made up based on the popularity of The Mask movie. Loki's magic mask is purely fictional for the movie. Over time, the relations between Loki, Odin and the mask blended together as the movie became part of the public consciousness on Norse myth.
It may be because both Loki and Odin are shapeshifters that masks have come to be associated with them, but there's no evidence from the actual myths that they wore them. Odin typically is blind in one eye, because he threw an eye into Mimir's Well to drink from it to obtain wisdom. There is apparently a popular Norse myth work called The Masks of Odin but the title appears purely metaphorical.