In Norse mythology, the red squirrel Ratatosk is said to live in Yggdrasill, the World Tree. He was a messenger who carried news and gossip between the denizens of the tree. In particular, he ferried insults between Veðrfölnir, the wise eagle who lives at the top of Yggdrasill, and the dragon Níðhöggr, who inhabits its roots in the underworld.
In England from the end of the Ice Age up until medieval times, it was said that a squirrel could travel across the entire country through the ancient Wildwood without touching the ground once. These would, of course, have been red squirrels.
Grey squirrels were introduced in England from North America in 1876 and became very popular with the Victorians, particularly the Duke of Bedford who imported a large number for his park at Woburn Abbey. Sadly, they drove back our native reds, which now can only be found in protected areas where the forest conditions are ideal, such as the Isle of Wight and parts of the north west of England.
Squirrels have been used to symbolise a number of things in the past. In traditional needlework samplers, squirrels denote mischief and were particularly shown in embroidered scenes of the Garden of Eden. In native American traditions a squirrel represents trust and thrift. As a spirit guide, it can also mean that a person is caring, nurturing and always on the go.
One website I looked at said:
"SQUIRREL - teaches us to gather and prepare for the future. Squirrel, in preparing for winter, gathers only what it needs. This medicine teaches us to discard not only unnecessary physical objects but those negative beliefs which limit our trust in love and abundance."This surprised me. I've seen squirrels take huge numbers of nuts from my bird feeder and I very much doubt they only gather what they need. I've watched them bury caches all over my garden and not only am I quite sure they forget many of these hiding places, I've also seen crows follow squirrels about digging up things they've just buried.
For more information about squirrels in folklore: