I can't prove or disprove any of the others' comments, but I can shed a little light on the cold issues.
I am due to have surgery soon and was told to change to very low carb diet (100gr daily) for 2 weeks leading up to the operation.
I found that after about a week (some people tell me they had the same issues within a couple days or so) I was constantly cold and had a metallic taste in my mouth whenever I ate or drank anything. It was awful! I was sitting in my sunny, hot flat (it's summer, after all) in sweats, a hoody, woolen socks and a lap blanket.
At first it was my whole body that felt off. After a while it was just my hands and feet, constant but not too terrible.
At this time I was also having a hard time managing my BG levels - I had 6 hypos in 11 days and one near-hypo attack on the 12th. It didn't seem to matter that I decreased my insulin dosages - I still kept dropping below 4.0 (closer to 3) and nearly passing out.
Whether it was ketosis I'm not sure, but my diebetic nutritionist suggested I increase my carbs by *up to* 50% to combat the side effects. Once I adjusted that a little bit (I never went past 25% increase and felt perfectly fine with that amount) things went back to normal. I'm still eating a very low carb diet (125gr) and things seem to have progressed well.
Bottom line, it seems that lowering your carbs does lower your body temperature, but apparently it isn't necessarily a bad thing (though if it gets to the point where it hinders you you should consult a doctor.) And even a small increase in carb intake seems to help balance the body temperatures. I'd discuss it with one of your healthcare specialists for a final opinion.
My best to you all and good luck fighting the good fight!
Cheers,
Shay.
Aah well, I'll have to stock up on cardies for the winter. 
