I get cold hands and feet when restricting calories AND restricting carbs. This is my two-fold experiment in CRON VLC Paleo, so far health and alertness have been great - sex drive and body temperature regulation have been kinda meh (compared to higher calories VLC paleo). Weightloss, as expected, is rapid (even though due to my previous year LC, where most of my water is gone).
It's a rough trade, but my work performance has been outstanding when eating 1400 cal/day instead of my normal 2400-2600. I just have to remind myself to re-feed with higher calories once a week (and the cold hands/feet subsides for a day or two after eating higher calories). I live in Florida, so the cold hands/feet is only an issue when I'm going to bed and when I'm waking up.
You didn't mention your sex. Females may have a tendency towards anemia more often than men, my wife has dealt with it for years. Her hands and feet feel like icicles at night.