I doubt a large capacity battery is required. Bicycles don't have to deal with a 100km/hr wind chill factor and the OP really just needs an ocassional input in maintain a comfortable temperature. A motorcycle rider is stationary. A bicycle rider is working and generating body heat.
My lighting system is 12V, I'm using 3S1P Lipo cells as well as AA's. Lipos are available in a variety of capacities and formats including hard-case versions. Obviously my experience is different than some other people. I've run up to 100W off a 5.6Ah RC battery without it even getting warm. And I have no issue carrying it in an inside pocket. These are rated for 165A CONTINUOUS USE so anything less than 10A amps is barely taxing its potential. The battery isn't much bigger than an iPhone and would probably be good for the day. If those gloves were run continuously at 2A they'd likely be to hot to put on.