'Haar' is derivative in the Northumberland and Fife dialects from Norse/Dansk roots, and one will hear it used from Aberdeenshire to Whitby.
There is also 'Smirn', which also describes a tiny-droplet, soaking drizzle - which is one step up from 'haar'. It's the same stuff....

Just as the Inuit have close on a thousand words for snow, so do the Scots have a similar number of expressions for rain - not all of 'em repeatable on a family show!