Ken,
All my tractors are workers so i paint the hydraulic lines black. I just added a deere rear hydraulic kit to my 420 this weekend and one line was already painted from deere, and the other wasn't. so from that standpoint, i figure deere wanted them painted as well.
The oil cooler, i just blow it out good with air, and wash it with water. got to make sure you don' put too much pressure to it and bend the fins the over. You could take a smaller fine wire brush and carefully clean the cooler if you wanted. I wouldn't paint the cooler though, leave it natural.
I guess everything depends on what your gonna do witht the tractor. If your gonna use it, it's gonna get dirty, so don't go too overboard.
nick