In Finland we have sometimes below zero (celsius) temperatures even in summertime, during night, and we get along with our summer tyres just fine.
Summer tyres work good enough on pale asphalt even if it is minus 10 celsius.
The problems start when you have ice, frost or snow on the surface. Then traction is quite close to zero.
We use two sets of tyres here, summer and winter. No one uses all seasons (because we know they are crap all season...).
Most of us has studded winter tyres but for the mild coastal winter, many people now use studless witner tyres. As they do not have metal studs and they offer good traction on ice, snow and asphalt, they can be used early in the fall and long spring.
I can highly recommend e.g. Nokian Tyres winter tyres without studs for you:
http://www.nokiantyres.com/products
To get idea why we use winter tyres: