I've always thought the word Haar to have a Dutch connection,(suprisingly many Scots words have this origin as there was much interchange between the nations). My grandfather (from Fife originally but resident in Edinburgh) always spoke of the cold east wind haar, associating it with both mist and a cold east wind. The Scots dictionary definition tends to confirm this

"The word is of Dutch origin, coming either from Middle Dutch hare, a biting wind, or Frisian harig, damp"