I always stretch before shooting, but I don't think it's necessary to "warm down". When cycling I always warm down: it wasn't always easy after a race so we had a masseur

, but I always did a couple of miles "spinning" slowly to clear lactic acid and prevent cramping and stiffness after training runs or time trials.
I think that if you're putting so much effort into drawing your bow that you risk lactic acid build up, you're way overbowed

.
However, I think warming up is vital to avoid muscle or tendon damage to the shoulders. I go for nice long stretches in every direction until I feel the tendons "loosen" (20-30 seconds) and then a good bit of arm swinging to get a bit of blood pumped into the delts, lats and rhomboids.
I try to stretch at intervals during the shoot as well.
