Definitely not, in my experience.
In fact, I would go so far as to say that feeling cold is, for me, a sign of too high/low BG .
A couple of weeks ago, we were standing in the middle of a field, in the rain. Mr B was huddled in his leather coat, cold and miserable. I was in a light raincoat and no jumper and was warm from fingers to toes - that was when I knew I had achieved ketosis.
Can I ask, have you been reducing the fat in your diet? Or have you been saving up your carbs and having them all at once, as a treat? Both of those would mess me up, and it might take a few days to even out after that.
Actually, now i think about it, I associate being cold with a few things - low calorie diets (shudder), and hypoglycaemia (bigger shudder). Also having a virus (possibly a temperature). And too little physical activity in a cold environment.
Could you have been skating a little close to low BG? I think that hypos also lower my immune system - but I have no scientific evidence for this.