Low carbohydrate diets can slow thyroid and therefore metabolic rate. Since ketogenic diets are the lowest carbohydrate diets possible, you may want to get your thyroid checked, particularly T3, T4, TSH and rT3 to make sure you aren't suffering. It wouldn't hurt to get your estrogen and testosterone checked as low testosterone/elevated estrogen are signs of stress. If you're cold, it sounds like your body is under stress and your thyroid is taking a hit. You may want to consider significantly elevating your sodium intake, taking kelp for iodine...or eating some carbohydrate.
Don't put your trust in anyone on this forum, including me. You are the key to your own success.