Re: running on snow and ice, I am lucky in that I live in a place with a pretty dry climate, so ice is an anomaly (our snow generally stays cold and dry, which keeps it "sticky"). I have Microspikes but have only used them for hiking and backpacking (traveling across snowfields). I'm sure I would use them more if I lived in an icier place. I just wear my regular shoes (trail shoes) with wool socks and wear gaiters if the snow is deep (I have short gaiters). I do have a pair of studded shoes but have only worn them a handful of times; I just don't need them on packed snow. I focus on taking short steps and staying light on my feet. Running in the dark on snow is amazing (but then I really just like running in the dark and love running in the cold). If it's clear and the moon is close to full, you don't even need a headlamp.

If you have an old pair of shoes that you are willing to sacrifice to the winter running gods, you can try doing this to them. Low-budget studded shoes!

Ummmm, yeah. Running on snowshoes is really hard.

Edit: forgot to mention that I don't run on pavement, so I don't have any advice for that!