I do in the winter but it is because of psoriasis unrelated to diabetes

If it isn't too bad I will use any hand moisturizer, if it gets really pesky the Doc prescribes a topical steroid cream but rarely use that

Best bet is mention it to your Doc - it might be something treatable

Diabetes can cause skin itch/burn/rash if the blood vessels feeding the skin get damaged severely due to high blood sugar, but you would "likely" experience severe neuropathy in the feet/legs "before" it showed up on the skin on the hands (but not impossible)