Generator output is what is running your components not the battery. If you take from the battery more than the generator can replenish then you will have a flat battery real soon.
For improved cold starting i have used Motobatt units in several of my bikes with no issues. I use Oxford Sports v.7 heated grips on my DRZ with no problems with a 4amp (48w) load on full power setting, what is the power consumption of your jacket?
IIRC the DRZ battery was about £40 from Everything But Bikes in Chester.