I agree with those suggesting mittens......
I have three sets of proper running gloves that I've acquired at different times (Nike thermals, RonHill merino wool, and a pair of Mizuno cotton gloves), but the ones that work best for me are a cheap pair of fleece mitts that I got free when I went ice skating on a work social.
The mitts are great because although they are very loose fitting, my fingers seem to keep warmer for longer, but don't overheat as much as say in my Nike thermals, and because they super absorbent they are really good for wiping off sweat, wiping my nose, etc...
GO