I too have always had cold feet. For me, this is related to Raynaud’s and has nothing to do with diabetes - as a young child, my Mum would complain about having to buy thick lined boots which I grew out of by the next winter.
Warm socks help as does making sure my feet don’t get too cold. Or, if they do, not warming them too fast.
Chilblains are caused by blood vessels bursting when they expand too fast as they are heated too quickly.