The ice crystals are nucleating in tiny scratches in the glass. The pattern you see isn't due to single crystals growing outwards in an approximate grid. It's many individual tiny crystals nucleating separately along a scratch line.
The tiny scratches are presumably caused by you washing the mirror, and their relative orientation is down to the scrubbing motion you use.
This is of course just a hypothesis since I can't inspect your car mirror in detail. You can check whether I'm correct by examining the ice with a magnifying glass to confirm that you're seeing tiny clusters of unrelated crystals. Also melt the ice with a hair dryer (so it dries off the water left by melting) and you should be able to make out the underlying scratch.