Hey, there are crystals in my wine!
Those crystals in your white wine, and even in your red wine, are simply acids -- tartaric acid to be precise. Tartaric acid crystallizes out of suspension at cold temperatures. When wines are shipped, especially in the cooler months, they are frequently exposed to temperatures low enough to allow these crystals to form, and they commonly grow attached to the cork.
Much like the sediment of red wines, these crystals are simply extra stuff that the wine doesn’t need any more. They dissolve in your mouth so there’s no danger of being injured by them and they are relatively tasteless and certainly harmless.