Since this is a heat question, I will lead with we live in Alaska, where it gets pretty cold. We have heat but no AC, so cooling isn't an issue.
We just started pulling apart our smallest half bath. It sits off the main hallway, pretty close to our great room in a warmer area of the house. When we removed the vanity, we found a heat duct opening. It wasn't grated or rectangular like the other openings that are meant to heat the home, it is about an 8 inch circle with some mesh over it. It went right under the vanity. Any hot air would be going into the 6 inch tall enclosed base of the cabinet.
Under the house, after some detective work, we discovered that the duct splits into two at the very end of the run. One side goes into the master bathroom (which is always freezing) and the other turns into two smaller circular ducts that blow hot air under the half bath vanity and into the void around the jetted tub in the master bath.
I can kinda sorta see the reason to heat the jetted tub area. We are planning to redo the master bath as well, so that may come out anyway. But, is there any reason the heat needs to go under the bathroom vanity? We live in a very cold area, so I was thinking maybe it was to prevent pipe issues, but the heat isn't being directed towards the pipes, just into the empty, enclosed space under the vanity.
Does anyone have any idea why the vent is there? Do we need to keep it open?
I would love to close both of these off and try to get more heat into the actual master bath. Any thoughts?