We have a mountain or two here.
Highway Thru Hell for example. I took the Insight through there once in the summer, with a flat battery pack. Lot of time in second gear. But I'd do it again. My main concern with the 1st gen Insight in the mountains is ground clearance for snow. Plus, I am too paranoid about someone sliding into one. My 1.0L Firefly got me through the mountains during the snow in December a few years ago with no issues, I think as long as you are willing to put your thoughts of economy aside for the trip and be willing to pick the right gear and go higher RPM when the conditions call for it, then a lightweight little car with tall, skinny tires can go pretty much anywhere as safely, or safer than a 6000 pound pickup. Get a little sideways in ice or snow in the mountains in a Firefly and you can correct it, get a little sideways in an F350 and you better know what you are doing or it's going to be a bad day for you.