In the above picture Mike, my second run, that was just a thin pair of silk liners that were earlier under a pair of DHB 'Windstopper' cycling gloves during the bike leg of the duathlon... My hands were bloody cold but the Reynauld's did not come on until I was in the relative warmth of the car after the event...
Normally, for running I use a pair of purpose-designed winter running gloves that originally came form Amazon and have done really great service... Any decent running shop such as Up and Running, Runner's Need or even Decathlon will have something suitable and can advise. Look for ones that are fairly thick, very flexible, are windproof and feel soft and spongy... I end up wearing mine for about 9 months of the year!
They'll be useless to me for a long run on a freezing morning so I'll wear a pair of silk liners and a rather thicker pair of ordinary winter gloves...
This morning I'm going to try running in my cycling Lobster Mitts...
Tomorrow morning I'm running the MK Winter Half Marathon so today at parkrun will be a trial to see if I can keep my hands reasonably healthy in all this cold!