More times than I'd like, I've gotten caught in snow storms while traveling. Crossed the Siskiyous on I-5 in 4" of fresh, wet snow heading South at the end of Jan one year. I was really happy to have ABS on the FJR that trip. Got caught in a freak snowstorm heading over a range in OR in mid June on a FZ-1 and ended up dumping the bike three times before I finally got a clue and turned around. Was only a mile from the summit, and the detour added 125 miles to my little day trip ride, but a pick up had just passed me going down hill and stopped to tell me it was worse on the other side of the pass, so I followed his tracks back down into the rain, and was never so happy to be riding in the rain too!
Rode about 100 miles in 20F temps on snow that had fallen the night before in NV, coming from Beatty to Hawthorne, NV. Was fine until I came over the hill South of Hawthorn and it had warmed up... glistening roads of wet ice and packed snow. Tossed the bike in a low side, slid for a ways and then picked up the bike and while doing an assessment of myself and the bike, the plow came by. Followed the plow into town and got some coffee at the McD's, then made some minor adjustments and rode the other 800 miles home to Portland that day/night, having lost the windscreen and both mirrors, then my electric jacket liner died in Ashland, making the remaining miles home in the dark very, very cold. Took a 40 minuted hot shower when I got home to warm up.
I try not to look for it, but will deal with snow, ice, hail while on the road and usually keep going unless it gets stupid or the wife is with me. Left on the last long trip with 25F and starting to snow, but was heading South and knew the worst was forecast for later in the day locally and better/warmer farther South, so left anyway. No issues.
We did get stuck in Fort Stockton, TX with 4.5" of snow having fallen the night before. I might have left on my own after noon or so when they opened the interstate again, but with the wife, we waited until the next day after it had warmed up and most had melted off. Only a few spots of ice on the interstate.