What a bunch of huff and puff. I admit riding a bicycle is a great way to stay fit, but all that dopamine seems to affect your ability to reason. There's nothing safe about riding a bicycle on an ice-and-snow-packed country road. Academic credentials and a pair of speedos isn't much protection from a motor vehicle.
Snow and ice are just part of the mix on today's roads. Drugs and alcohol are out there 24/7. Modern automobiles are chock full of distractions. We've got cell phones, global positioning systems and the list is endless.
You stated at times its difficult to pull your bike off the road. There's a reason for that. It's the same reason they don't have bike racks at rest stops. Roads were designed for motorists, but let's review your request in this day of the multi-tasker.
When a motorist approaches you and your training partners we are to pull over, offer a friendly hello and let you pass safely. Would you like a refreshing glass of Gatorade with that, your majesty?