There are "all season" tires available for Corvettes and some are speed rated at W (168 MPH) and Y (186 MPH)
Here are a few to get you started:
BFGoodrich g-Force Super Sport A/S
Continental ExtremeContact DWS
General G-MAX AS-03
Goodyear Eagle F1 Asymmetric All-Season
Michelin Pilot Sport A/S
Michelin Pilot Sport A/S Plus ZP (run flat)
These fit my C5, but there are A/S for others. I don't know about Virginia, but quite a few states require A/S or M+S tires in bad weather. Which is meaningless unless there is an accident.
Go to Tirerack, discounttire, and others to read the reviews. When you have them balanced, as it simulates weight, I recommend the Hunter Road Force balance. Just ask if the installer has a road force balance.
Personally, as I have a 4WD truck and hers is a AWD, I don't drive my Corvette in snow.