What does it mean to "sniff at someone?"
Solution 1:
A sniff (drawing air through the nose in a short, audible inhalation) is sometimes used as a sign of contempt. See Dictionary.com:
4. to show disdain, contempt, etc., by or as by sniffing.
Nynaeve is disparaging Elayne's comment by the sniff. Note that a sniff can be a haughty way to express disdain, as if words would be too much to waste.