From cold, irrespective of what temperature it is around you, it takes roughly two miles for tyres to heat up to an improved/effective level.
So on a cold day it'd take two miles for the mpss to warm up to make use of its improved grip. The alpins would take the same two miles but they'd still be safer from the get go. If its under 7°c outside air temp then the mpss would never have as much grip as the alpins. No matter how much or hard you drive it.