A socket on the handle bars? That'll be fine until you lift your hand to wipe your visor... A slack will just be crying out to get tangled in steering or caught on another vehicle as you filter.
With my Gerbings, I have the socket wire poking out from under the seat. Controller is cable tied to waist of jacket, then rest of wires going down sleeves. Glove plugs are tucked in by wrists, and I simply have to lean down a plug controller in by my left leg. Thus the only wire going 'everywhere' and on show, is 6" beneath my left leg.
Some heated glove can be run off a battery, but they're expensive and bulky to slot into your gloves.