Anything you wear on your face is going to wet out, there's nothing that doesn't except for the subartic mask they sell at REI because it has a plastic cup that stays clear of your face.
The best thing you can do is wear merino wool. Even if it wets out it stays warm, and wool is naturally antimicrobial so it doesn't hold bad odors, which is important when you are breathing it in all day. I like to wear the icebreaker balaclavas or a wool "buff" neck tube and use it like a face mask. The buffs in particular come in nearly every color or style you could want: http://www.buffwear.com/buff-adult-headwear/wool-buff