Most of the "hospital software" (groupware) you may find is built for Windows. Most of the orchestration infrastructure running the hospital is Linux. If you go to a hospital and see nurses unlocking cabinets with badges, or scanning to track movement: Linux. Same with Pharmacies.

User interface junk, most likely Windows.

I know Kaiser has an extensive end-user system running Linux desktop based on whoknowswhat for mobile device carts and whatnot. Worry less about the desktop, and more that Linux is healthy enough to be running literally everything else, from the networks, to the physical doors in the building.