Everyone has their own way and i'm sure most methods work fine. I got to meet author/restaurant owner Jessie Griffiths and he later told me he never puts meat directly on ice ever. Meat in trash bags, on ice.
I only have a 30-06 which is fine for most things but I wish i had something lighter as well for newer shooters. I've had young nieces and nephews put off by the recoil.