Acting stupid will get you in trouble with anything anywhere, that's facts of life.
You have enough power on cold tires and cold road, it's ice.. two of us already said this. My Bolt-on & Tuned C5Z06 will absolutely float the rear tires out from under it as I'm going through the RPMs even in 3rd, cold street tires are trash. On scale it was 3085lbs, lighter than that C7Z06 all day. Power and no *ss to plant it, not a good combo to the rookie drivers.
Let me explain the factors that are relevant where I asked if you have the experience:
Corvette Z06 is damn near a 50/50 bias car. Excellent for cornering and road course. Short wheel base helps here too. However, with both combined, you will lose it faster and the rear with half the chassis weight is slinging around the front fast. Steer into it quick or ride out the wreck. Add stiff suspension to amplify any bumps or uneven road surfaces. Can become unstable quickly.
Front engine car with more of that weight up front and longer wheel base, much easier to control.
I play with both of my cars enough to feel them out, BIG difference between my Monte SS and my C5Z06. I have pushed both where I know what they can do. That's how you learn. Z06 on street tires with all the factory assists off is asking to wipe it out.
So yea, experience is relevant here, feel free to divulge yours like I asked, we are just discussing it. If you never have then just say it, Corvettes are fun cars. You can say "may or may not have done", the point is these cars get out from under you MUCH faster than you think. Takes knowing your car to another level. First is respecting it, then learning it.