My understanding, and correct me if I'm wrong, is that with a diesel system it's not good to do short starts and stops if it is not up to normal operating temperature to avoid carbon buildup since things aren't hot enough to burn it off. In this case I would let my truck idle if it's only going to be a minute or so in a store or something. If I leave work and drive half a mile and go inside to pick up lunch, then drive back I would let it run, especially if it's really cold out. Otherwise I shut it off.
With the tractor it just depends on how frequently I would be getting off to do something and for how long. If I were repeatedly getting on and off to do something I feel like it's best to let it idle for a few minutes rather than put a beating on the starter and battery. Sometimes if I feel like the tractor is getting a real workout I'll let it idle for 30 seconds or so then shut it off and let it cool off for several minutes, sometimes even opening the hood. If I feel like I need a break I figure the tractor could use one too. Then it's back to work.
With the tractor it just depends on how frequently I would be getting off to do something and for how long. If I were repeatedly getting on and off to do something I feel like it's best to let it idle for a few minutes rather than put a beating on the starter and battery. Sometimes if I feel like the tractor is getting a real workout I'll let it idle for 30 seconds or so then shut it off and let it cool off for several minutes, sometimes even opening the hood. If I feel like I need a break I figure the tractor could use one too. Then it's back to work.