yes, Stig, the pliability or softness of the rubber at various temps is a big difference between pure summer (high performance) tires...they get as hard as glass at freezing temps...even 'all season' rubber gets very hard around 40 f...and winter rubber, the new kind with the mountain snowflake symbol, will stay soft down into very cold temps.
It's also why many true winter tires are not to be driven when temps reach a certain level (50's f?) as their wear rate will increase significantly.