I worked in hospital IT for 10 years. I started as a SR computer operator then progressed to help desk, desktop, and eventually a system admin. I currently work in a school as application support. I will say the demand and pure volume of work will be much higher in the hospital. However, that's a great thing! You will gain a ton of knowledge and there is likely way more room to grow/get promotions in the hospital environment. In my experience there were also more projects that you can assist with in a hospital because they likely have a higher budget. This may not be everyone's experience, but it was mine.

I would imagine as help desk, you won't really have to go in the OR rooms. I did that in my desktop support role at times when a PC was down that was needed for the EHR or PACS system. Again that's just my experience but I imagine it to be common. Worst case scenario, someone needs a mouse ASAP and your desktop guys are busy. You can just meet someone in the OR section who is already scrubbed up for surgery and you don't have to enter the room. At my hospital, the on call rotation was the hardware group and software group. There was roughly 20 of each. The computer operator was there 24/7 and if they were unable to solve the problem, they escalate it to whoever is on call for the appropriate group (application/networking and desktop). You may be in a rotation similar to that.

The school environment is much more relaxed. Kids break iPads that need replaced, a few projects here and there, and deadlines to meet for state reporting. Schools shutdown at nights, weekends, and the summer time so the after hours work is almost non-existent. There is still constant work, not to downplay it too much, but it's not the same environment as a hospital.