Everyone knows pictures of classic cars (with wire wheels) rallying in the snow - today as well as in period. MGBs, E-Type Jaguar, Austin Healey,... all of them were most famously confronted with snow at some point, often during the Rallye Monte Carlo.
Snow = unbalanced weight
While it looks quite unproblematic on these pictures, after a longer drive in the snow, there will be a lot of and in between the wire wheels. Once frozen on, it adds a lot of weight, even worse, if pieces are flying away, there is a lot of unbalanced weight on your wheels.