For running, get thin gloves that keep out the wind chill. Your body will heat itself up, including your hands, so all you look for is decent wind protection. I did some trail running in down to -10C, and thin running gloves were sufficient.
If you want bells and whistles, get gloves with reflective elements. In winter, chances are you’ll spend some time running in the dark.
Similar in Ireland. Had my kids’ passport applications co-signed by their school receptionist.