If you MUS go, go with caution...
That said, it's not a bad idea to keep an eye on the shoulder.... I've found that if the roads get glazed over from that wet/heavy stuff being packed that it is much better traction on the shoulder with some depth and LESS ICE....Just adjust speed accordingly
Heck, many years ago we had a wicked ICE storm after about 8" of snow.... It took me 3 hours to make the 15 minute drive to work, I made it by the driving shoulders and front grassy areas of folks yards... just dodged mailboxes is all...