On a signet ring I wear, there's the family motto surrounding the 'family crest' – an image of a hand "pruning a vine tree with a pruning knife...".

I've always wondered where are grapes grown in Scotland? I thought it may be too cold for viticulture.

Maybe it has something to do with the Celts moving over from mainland Europe?
In heraldic law, there is no such thing as a 'family' crest. The crest belongs only to the person to whom it was issued – ie the Chief. 

However, that stated, when one wears the Chief's crest encircled by a belt and buckle inscribed with the Chief's motto, it indicates allegiance to that Chief... ours being James C A Burnett of Leys. So I gather by wearing my signet ring I'm pledging allegiance to him.

The Burnett motto

...is Virescit vulnere virtus – Courage flourishes at a wound– and is the same as for the Stewarts.

It probably owes its origin to Mary, Queen of Scots, who is said to have embroidered it on some material during her imprisonment by Elizabeth I of England.
Here's something...

The Burnett castle, Crathes Castle, is haunted by a headless ghost named Ewan... which is also my brother's name. Interesting.

And I'm told that grapes grow in greenhouses at Crathes Castle.