Well I'm not a runner, and I see people around here running in shorts when temps are in the 40s (fahrenheit, where freezing=32) which I think is nuts. So I can't give specific recommendations.
But I can say that there is a big difference between winter weather in LA and winter weather in Chicago. Chicago is way colder, and the wind off Lake Michigan can be very strong. So if you were thinking that you need to prepare to dress in layers, you would be right.
For cycling in colder weather, I have a pair of windshell gloves (with no liner material for warmth) and a pair of thin wool glove liners. I find this combination to work well and be nice and versatile. Since neither pair of gloves is bulky, they pack well.
A base layer top would not necessarily be bulky. I have some wool long sleeve base layers that are quite thin, and I recently bought several of these wool tank tops which are also thin.
http://www.teamestrogen.com/prodIC_100231.html
- Gray 2010 carbon WSD road bike, Rivet Independence saddle
- Red hardtail 26" aluminum mountain bike, Bontrager Evoke WSD saddle
- Royal blue 2018 aluminum gravel bike, Rivet Pearl saddle
Gone but not forgotten:
- Silver 2003 aluminum road bike
- Two awesome worn out Juliana saddles