Would they not send the TC in to a spaz?...... especially being winter when your more likely to have slippage
TCS doesn't really care as long as you drive to your own and your cars limits. If you push past that then you're not driving correctly, so for the purposes of using winter tyres for more grip in the snow then you really shouldn't be pushing any way.
For once I wasn't even being sarcastic! Truth be told though if people want to start mucking around with the only things keeping them on the road, and especially in the winter, then they probably will anyway. Personally I don't feel it's worth saving £50 and risking the car, but to others they're happy with that risk. Each to their own, and I genuinely mean that. I've said in the past njthat I'll only give general advice on tyres now anyway, after the abuse I've had in the past.
So, in all seriousness, they probably will be okay as long as you don't drive like a tit.