I can see wanting to warm the hydraulic oil for a hydrostatic tractor.
On cold days, I sometimes turn my PTO on, with no load, to get hydraulic oil warming. I doubt that it heats much just turning the PTO shaft. Some people turn the steering until it goes into relief. Oil running through a relief valve heats up considerably.
To me, idling an diesel when started seems like a poor way to warm up the engine. A diesel has no throttle plate, so you’re sending the maximum amount of cold air into the engine with the least amount of fuel. Compression will warm some, but not most effective.
By putting a load on the engine (by moving and starting work) you’re at least putting more fuel (and heat) in the engine at a given rpm (air flow).
It really depends on what you mean by cold. At 30F engine oil and coolant may start to warm at idle, but at -10F, results may vary.
I start tractor, let it fast idle for a minute or two, then slowly putter out of the barn, all the while slowly bring up rpms.
IMHO, it’s important to me for the engine to heat up slowly so that expanding metal parts adjust to each other slowly.