When people refer to 'white hairs', it is usually when a horse with a non-white coat develops areas of white hair where previously the coat was a different colour.
It is important to pay attention when this happens because they are usually caused by one of two things:
Pressure – this can be from equipment or clothing such as rugs or saddles.  However, it is very unusual to get areas of high pressure under a BALANCE saddle because they are designed to be fitted wider than the horse’s stationary shape.  With a BALANCE saddle, risk of pressure would usually only be an issue if the saddle was padded very incorrectly, or if an inappropriate width was being used (too narrow, so that it fits like a tight conventional saddle). Pressure tends to create an area of all-white hairs.
Friction – Friction occurs when there is repetitive movement/rubbing of the skin and/or coat(and ruffled hairs are an early warning sign of friction). Friction can cause patches where some of the hairs are white, while others are the usual colour of the coat, creating a ‘roan’ effect, or it can create areas with all white hairs.  A sprinkling of white hairs is a warning sign.  Friction will cause skin soreness and the horse will usually hold the back away from the saddle in an attempt to reduce that soreness.  It is important to check how clean the horse and the underside of the pad are.  Dirt, grit or sand from the arena can act as an abrasive if it is in the horse's coat or the wool of the pad.
In either case, the cause of the problem needs to be identified and remedied, as it is sign of a significant problem.