What are you expecting? You just put on narrower tires with a deep snow tire tread compound that cannot take much heat. I run those tires on stock wheels and they are pretty good as far as snow tires go. I have had a lot worse handling snow tires on other cars. There are better handling snow tires, but they will be worse in the snow.
It is a tradeoff. Forget about go kart handling in the winter. But with PS2, forget about driving in the snow.