Oh! Don't leave her like that, get out the brush!
I've driven in worse conditions than that and have not needed any weight in the back of the car. If you drive smart, keep the TCS on and don't challenge the car's road sticking ability on a slick surface, you'll be just fine. If you don't have or don't get TCS, just be more carful and toss a sand bag or two in the trunk. Worked great for my old FOX.
I'm a little nuts and I'm known for passing the odd SUV, 4X4 cars/trucks in 3-5+ inches. I know what the car can handle and it's not my problem if a driver of an ATV doesn't have enough trust in their car/truck to go past 20MPH.
The P Zeros are THE best all season tires I've ever had on a car. Even with no water channels, they stick very good in the rain and hydroplaning is pretty minimal.
TJ