Bridgestone's snow tyres are very much snow and ice focused. Total mooosh on tarmac though, and even worse if it is warm IMHO. They've tried to make amends with the REV01, but I won't touch them (living in Tokyo, we only see snow on the ground in town 3 or 4 times a year in a heavy one). But if I lived in Hokkaido, I'd probably give them a serious look. As it is, I drive to the snow fields a lot, so use Michelin or Pirelli snows which are a bit better on tarmac for the motorway and still decent on snow and ice.

Anyway, I digress. IMHO, it is possible for the car's handling to go a bit south, but not to the extent you mention unless something is wrong. Perhaps the pressures are totally out and it was abt 30 degrees or as someone mentioned diesel?

Keep them for a big snow storm though, and you may be surprised how good they can be in those situations (make sure they are in good nick though, as they go off when old and hard - 5 years is defo the limit).

HTH a bit - IMHO go get some decent sports rubber for your baby