I wonder if there would be any benefit?
Googleing to answer that question produced an article claiming (without evidence backing it up) that:
"Research has shown that a restricted intake can reduce the service life of a gear pump by 56 percent".
Both the HST charge pump and the main hydraulic pump draw through a strainer. The main pump flows oil at all times when the engine is running although I believe the HST pump is disengaged with the clutch. It stands to reason that cold oil won't flow through the strainer as readily as warm oil.
So if the above is true, then it's possible that warming the transmission oil with some sort of heater before starting the tractor would reduce wear and tear on the pumps. It's also possible that the HST charge pump life could be extended by keeping the clutch disengaged until the oil has warmed.
The other thought that occurs to me is that the hydraulic oil filter probably has an internal relief valve so that the filter media is bypassed when plugged. So it's possible that unfiltered oil might be bypassing the filter and reaching the HST motor until it's warmed up enough to pass through the media. That's probably less of an issue with hydraulic oil than motor oil though -- motor oil is exposed to far more contaminants.
So, yeah, to answer my own question: It might extend hydraulic system life to install some sort of transmission heater if the tractor is regularly started in cold weather. It's probably even more important to use a high-quality synthetic hydraulic oil.