I'm a veteran of high school/college indoor competition in New England. I enjoyed interval training on winter streets, often the highlight of a cold winter day. I'd run with temps as low as 10F. I was running the half, 1000, mile and 1500 indoors, also the two-mile relay. Yeah back in the day.
So, it's all about layers. This applies to your UNIT too! Yes you will wear that outer layer that covers your legs (sweat, tights, etc.) For 10 degree weather, I'd also wear two pairs of low-rise briefs, fitted sweats, and trunks over that. That is 4 layers. The triple layering starts at 20F. Be sure to apply lotion/vaseline to your inner thighs. If it's windy, you want that out layer to be a windbreaker layer, torso and legs both. A few thin layers is better than any bulky layers.
Good luck and have fun.