I learned my lesson yesterday!
My bad weather commuter with studded tires had a flat that I'd been too lazy to fix given the dry weather. It was raining and ~34F, so I thought I'd be okay on my good weather bike with road tires. The temperature dropped a bit, and the ground was already frozen. After the second time nearly going down on my way home, it was time for hike-a-bike.
Studs might be slow, but they're faster than walking or going to the hospital.