I grew up in eastern South Dakota, so know a thing or two about dealing with the cold.
The lowest temperature I’ve ran in was -30*F and in my hometown the average high does not get above freezing for a number of months.
When it comes to running outdoors in the cold weather the primary consideration is layers.
In regards to my hands, I use the below options quite comfortably. It’s nice to have the cheap gloves to wear by themselves if it’s just a little cold or I can wear them and a thicker pair if it’s colder.
Note: The below links are Amazon affiliate links. I do not run ads on this site but do use affiliate links. All proceeds help support the website hosting.
Cheap Gloves (liner or 30’s)
Pearl Izumi Wind Resistant Gloves (20’s-30’s w or w/o cheap liners)
Pendleton Mittens (nice by themselves or with 1-2 pairs of gloves under)