Reddit mentions of Alki'i Suede Palm Wool Thermal Insulation Fingerless Texting Work Gloves with Mitten Cover, Gray, One Size

Under layers are important. Long johns and a thermal-knit top under your regular clothes. You don't need to splurge (I usually buy Hanes) but if you want to splurge, Under Armour is great stuff. My running gear is all UA, and then regular long-sleeved tee and sweatpants over that. Of course, only when it's really cold, so far it hasn't dipped much below 40. But the daily stuff I wear to work/out-and-about is just whatever I found at Target, and it works.

I use these gloves and swear by them. Super warm, and with the fingerless option and thumb hole you can easily use your smart phone. And the cuff rolls down pretty far up your forearm, so you don't have a gap between your coatsleeve and glove where wind can get in.

I'd recommend a hat with ear flaps, I have one lined with fur, and when it's far below zero and there's a biting wind off the lake, you can wrap the ear flaps under your chin and wrap a wool scarf around your face and neck over the flaps and no wind gets in. But a really thick wool beanie would probably be OK too.

Boots, you don't want anything that isn't completely rubber on the bottom (lined inside, of course). Not just a rubber sole, a rubber bottom, like this. Any type of fabric will get wet when walking through snow and puddles and then your feet will be freezing.

Those big bulky sleeping bag coats are pretty amazing, and enough people wear them that you won't look like a tool, but if you dress in layers you can buy something more professional looking and still be warm.

Of course all that stuff if for the super cold days, which there usually aren't more than 10-15 of. When it's above zero you can just dress in layers and wear normal gear and be fine.

ETA: ignore all that stuff below. Tested both out today and my ends eventually froze in both liners (with gloves on top and mittens on top of those) while everybody else's hands were fine. So I need to figure out some serious ski-gkove type replacement anyway.
**
Glove liner showdown. I bought (on better sale than Amazon) icebreaker 98% merino wool 200gram glove liners and smartwool 45% merino wool glove liners and I have 30 days to return one pair- anybody have experience and think one would make the better running glove liner? The icebreaker are higher % wool, which seems good for what I need in a liner, even though the smartwools are much thicker.

For context, my hands have been getting cold even at 40F and get really cold w frostnip or Reynaud's type symptoms under freezing even though I tend to wear these head running gloves under these wool convertible mittens w thinsulate. I think my hands still get cold because I sweat just as much in winter as in summer. The head gloves get soaked and synthetics are cold when wet, so I'm thinking a merino wool liner underneath could make a perfect trifecta? If you think something else would work better, I'm all ears. 

Sidenote: ny running co/jackrabbit are having some great sales on gloves/winter stuff/outerwear and on summer stuff too (shorts, tanks, short sleeves, capris).