You ask a number of questions.
I run year round and did so in Illinois and Utah so there were times it was cold and/or snowy or icy.
The temperature range you give is pretty broad.
At 30F, I'd probably wear a single layer. Long sleeve tech-shirt, tights or nylon wind pants, knit gloves, and possibly a ball cap.
At 10F, I'd wear multiple layers. Running glove-mitts, a long-sleeve tee with another shell, heavier running pants or tights under wind pants, a knit hat, and a neck gaiter. I try to wear socks that prevent bare skin showing in these temps.
It also depends how hard I'm working and what other weather factors are significant. Running up the mountain, you're either working very hard and risk overheating, or throttling back the effort. Your effort running back down will be lower (and possibly into the wind). If you are soaked from the effort running up, you'll be very (dangerously) cold coming down.
Much of my gear is no-name stuff I picked up on clearance and at end-of-seasons.
If I were prepping for this run, I'd probably start with a single layer (long sleeve tee & tights) and make provisions to carry a pair of nylon wind pants, shell, heavier gloves, and the knit hat. I don't want to start out running in the heavy gloves and knit hat and saturate them.
I'd also protect my face with vasoline, wear sunglasses, and carry lip balm.
As for shoes, I'll often wear "trail shoes" to run in snow. (My "trail shoes" are usually grey/black versions of road shoes with a little more tread, not highly technical trail shoes.)
After running, get into dry clothes immediately. Once you've showered, use some lotion all over because the cold, dry, air is hard on your skin.