The biggest problem I have found with F1s and snow is braking. Obviously you avoid braking if at all possible on snow with unsuited tires. But as soon as you find you have to break on the F1s they turn into ice skates, no matter how gently you apply the brakes if you aren't going absolutely dead straight then you're headed to the kerb in a sideways slide.

Having ABS that you can't switch off doesn't help.

Still, at least the Scooby on F1s deals with snow better that the MX-5 on F1s does. Every roundabout ends up being taken with the car at 70 degress from the direction of travel, whether you like it or not.