I don’t know how to ask this without it seeming like snark, but as genuinely as I can ask (and with the assumption that we otherwise agree there should just be a door):

Why don’t you just turn on the heat in the room?

Locality and humidity.

I also don't mean to be snarky here, because I'm not sure how to say this in a way that can't be interpreted that way and feel like I'm just explaining being human...

The answer is really just physics. The feeling of comfort is generally about differential in temperature, not absolute. (That's also a logarithmic relationship too) So to have that nice feeling of stepping out of a hot shower then the room needs to be a decently high temperature. Mind you, you're also wet. This makes the temperature differential more influential. So two things happen when you dry off. You no longer have that water to transfer and maintain heat and you've also cooled down a bit. Now when you walk into the normal room temperature the differential isn't so bad.

If I turn the temperature up in the whole hotel room I will then have to turn it down. Now that introduced AC and we have the opposite problem... Plus both get rid of humidity.

To be snarky and try to be a bit humorous:

Haven't you ever noticed that 100F/38C is "hotter" and more uncomfortable in a humid environment than in a dry environment? Haven't you ever noticed that 15F/-10C is "colder" in a humid environment? Haven't you noticed that being in a hot tub or sauna is comfortable but if it was that temperature outside you'd be cursing the gods? Haven't you noticed that in the summer 50F/10C is cold and most people won't wear a short sleeve shirt yet if it was the winter that's a nice day to go out and wear shorts? Haven't you... lived in a body?

It's winter man, here's a trivial experiment for you:

  - Heat up your house:
    - Shower with door open
    - Shower with door closed
  - Don't heat up your house:
    - Shower with door open
    - Shower with door closed