There are other animals who are talented about making weather predictions, particularly winter weather.  I love weather and folklore so this subject is always on my radar!

Here's a list:  https://www.farmersalmanac.com/animal-weather-folklore-26461

And here are a few more:  https://www.farmersalmanac.com/20-signs-of-a-hard-winter-479

I have never seen a gray squirrel in the area of the country where I live now (in the mountains and hills), and we have only seen snowy owls farther north in our State, around where my hometown is located, and my husband's hometown, too.  I guess they prefer haylofts to mountains! It was very, very flat in the area where both of our hometowns are located - - so flat you could see the end of the world, but we sure saw some gorgeoous sunsets!  But the wind never stopped blowing on that flat prairie, it seemed.

Also, my State has very few oak trees so acorns are not plentiful on the Northern Great Plains.  I suppose it gets too cold for too long or something.

And lastly, I was raised around lots and lots of cattle all my life and they seem to group together in bunches when bad weather is coming, and that goes for summer as well as winter.  If they are in the barnyard in a corral, they will gather near the barn in a corner of the corral and pack themselves in tightly if the storm is near or if it's going to be a long, windy storm.  That's an observation my family made long ago.  We had just too many cows and bulls to put them all into the barn and various other shelters, so some of them simply had to fend for themselves.  It was the job of my brothers and I always to make sure the littlest critters were inside the big barn, the secondary barn, the lean-to or the salt shack.  Sometimes we had 200-300 calves all needing a warm place to be and there wasn't always room indoors so we would pile up bales of hay and create makeshift shelters if we had a banner year of calves!  Momma Hereford cows most always calve in mid to late February, all of March, and early to mid April.  They and Mother Nature seem to have conspired to pick the coldest and windiest part of the year to bring new life into the world.  Not sure what Ma Nature was thinking there . . .