I walk in icy conditions usually but I won't run in them. Most of the time my dog and I walk three times a day so our last walk is in the dark. When it's more slick out we usually don't leave the neighborhood so walking it so often helps me remember where the slickest spots are and we just slow down. If a whole stretch of sidewalk is bad we will walk in the street but I try to stay on the sidewalks, especially after dark. I do have Yaktrax chains but I hardly ever use them bc it's very rare that the whole neighborhood is an ice rink, just certain spots, and wearing those on clear cement or blacktop isn't great.
I am like you, I really need that morning walk especially or I feel all messed up. If I miss the other two walks I deal with it much better than missing the morning one, but not enough time outside really messes with my whole self.
Like Erica, I won't run outside in icy conditions bc it isn't worth the risk of injury. You have a lot more momentum going with running! I am so grateful for my treadmill for winter running.
As my mom used to be sure to tell me, be safe out there!