Several times each year I day-trip at altitudes exceeding 4000 meters and I don't take it lightly. Air resistance is greatly reduced, so brakes do extra duty and the acceleration is surprising. It's hard to avoid snow flurries, but I wouldn't ride in muddy or icy road conditions. In short, I would not attempt that crossing. But I'm older now and have a different viewpoint.

A relatively minor annoyance compared to rims icing up is the rear cassette icing up, leaving you with only one gear. Choose that gear wisely.

Use the "Bagtex" trick on your feet for cycling in snow--bread bags or similar over your insulation and inside your shoes. For daytime temps just below freezing, good gloves should be fine, with plenty of breaks to warm your hands in pockets or on your torso.

Keeping water bottles and wet clothing from freezing while camping is another issue. I keep clothing under my sleeping mat, and water bottles under my knees, outside the sleeping bag. Shoes may need to be kept with the water bottles, too, and you might want a bag for them. Putting wet clothing back on in the morning is probably the most difficult thing in harsh weather camping.