How about a vest that circulates ice water from a cooler mounted on the bike? It'll keep your beer cold too.
I met a guy last yr that had just that and he built most of it. He bought a vest off ebay with the tubes in it - can't seem to find an example right now but will edit and put it in if I do - but the rest he built. He had a BMW LT and had one saddlebag dedicated to it with a cooler in there, and "I think" windshield wiper pump with electrical on/off on the handlebars, plastic tubing, and QD's to hook it up. He said it worked great and that the vest was the biggest expense ~$100 iirc. It also used up ice/icewater when hot so not sure how good it would be for LD.
Intriguing idea and being the type that likes to build shit, er, stuff myself I was thinking - what about using one of those 12V coolers that heat/cool - you know the type? You could even just pull the element out of one of those (unless someone here knows where to shop for those things) and put it in something better shaped for your specific purpose. That way you could still load with ice but it would take longer to melt down
Just another crazy idea that I think about sometimes.........
edit: Here it is - and yes someone has got a motorcycle application for $438 and shirt only for $139
https://www.ebay.com/itm/Blue-Cool-Water-Shirt-BCW-Cool-Shirt-/170693322313?pt=Race_Car_Parts&hash=item27be1d6649&vxp=mtr
https://www.ebay.com/itm/Motorcycle-Cooling-System-Cool-Water-Shirt-Cool-Shirt-/170653544495?pt=Motorcycles_Parts_Accessories&hash=item27bbbe702f&vxp=mtr
Great idea but don't know if it's practical enough......