I have tried it, many times, and it is exactly as I say.
A 2wd tractor, with massive treads on the back wheels, is not very good in snow either. A tractor with lawn tyres on is better.
Snow compacts into the small treads giving you lots of grip. With the knobbly tyres, the snow packs into the vacant spaces in the tread blocks, and the wheels start spinning,
It's more likely that my lack of snow practice was to blame. I stopped in the drift while the mrs went off to get something, and then when she came back a few mins later the wheels just spun. If I hadn't stopped there I think we'd have been alright, as it wasn't the depth that was the problem. I know for next time!
 
There is difference in the tread, a winter tyre has many more "Sipes" or small cut like patterns which can grab at the snow and thereby provide more grip, in addition to the low temperature compound which as you say stays softer at low temperatures. They start operating as designed at temperatures below plus 7 degrees Celsius. At temperatures significantly above plus 7 degrees, winter tyres can wear somewhat quicker than normal tyres.
This article from "Which" gives some details about the tyre construction:-
https://www.which.co.uk/reviews/new...yres-and-snow-socks/should-i-buy-winter-tyres

That is interesting. Never had the winter tyres myself, but I remember reading about the softer compound somewhere.

It's more likely that my lack of snow practice was to blame. I stopped in the drift while the mrs went off to get something, and then when she came back a few mins later the wheels just spun. If I hadn't stopped there I think we'd have been alright, as it wasn't the depth that was the problem. I know for next time!

In mud, or snow, or any slippery surface, never stop unless absolutely necessary.
 

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