mmm1a: the best solution I found when I was playing trombone in the marching band was to hold the mouthpiece in my hand when I wasn't actually playing. Our band wore white cotton gloves in uniform, so holding the cold instrument wasn't a problem (don't go there, Spaw!). If the band doesn't wear gloves, you might try rigging up a leather cover over the tubing and slide where the hands hold them. Some soft buckskin laced on would do nicely.

jeffp