Apparently the Prius has this problem, and the tyres are excellent to get it's fuel economy up, but useless in snow. Apparently if it detects a wheel slipping it cuts power completely for a second or two, meaing it's often impossible to get through small amounts of snow/ice.

I did read about an undocumented way to override this, it read like an old "U/D/L/R+FIRE" cheat code.