Almost all compacts use open centre hydraulic systems. When no hydraulics operated, the pump still pumps its rated flow from, and back to, to the reservoir. An open centre system works the same in gear or in neutral.
Hydro transmissions use the same oil as the hydraulic system. I think Hydro range selectors have a neutral that should be left in neutral when the tractor is warming up for safety reasons. I don't know if the HST pump pumps oil when the range is in neutral or not. However, they don't flow oil when in gear and 0 HST pedal. And wouldn’t help warming the oil.
A good reason for operating the loader and 3ph is to get the very cold oil out of the hydraulic cylinders and lines. I use a magnetic heater on the oil reservoir, so the oil starts out slightly warm.
I leave my tractor on block, transmission and battery heaters for a couple of hours if the temperature is near 0F or lower. I warm it for 5 - 10 minutes @ 1500 rpm, or until it stops puffing gray smoke. I also let it cool down @ 800 rpm until it starts puffing again.