As a Canadian who has driven in snow for 33 years "blaming the tires" is odd. Most of my life i drove on all seasons and only got "snow tires" 4 years ago because I get a discount on my insurance for having them.
The reason it is having issues is because it is attempting to accelerate too quickly for the road conditions. Perhaps snow tires might help a bit, but if it is unable to handle "all seasons" and a bit of snow.. that itself is a problem and snows may not fix it because they are not some sort of magic that suddenly gives you amazing traction on something slippery like snow.
If there is over a few CM of snow on the ground, i can spin my 2 yer old snow tires as fast as i want... Speedo showing 90km/h while i am hardly moving... All i need to do is disconnect the TC and press hard on the gas, the snows quickly lose traction and spin.
The human driver is obviously lighter on the acceleration due to road conditions and so less TC is needed.
If it needs to disengage so frequently in these conditions, its not FSD.