Can a shampoo box be built into a wall which is exterior of the house? I have a feeling without the insulation it will be cold.

I understand this is a rather difficult to answer questions and not sure anyone can answer it but me but thought I'd try. We are in the process of incorporating a room at the end of a hallway as a master bath (visualize yourself walking down a hallway and the master BR in on the left and you walk further and the hallway opens up to the left which is what will be the master bath). Eventually, the hallway's wall on the left will be "extended" to create the space and you will access the master bath through the bedroom. I would like to "wall off" this area sooner rather than later as we can then finish the hallway and call it complete. The only "bad" part about finishing the wall now is that all access to the room that will become the bath will be through the master BR. For several reasons, I'm wondering if that is too soon. I don't see us having to move in anything so large that we can't get through the remaining access but it will still mean a lot of in and out through the bedroom (tools, material, myself, whatever) just to work in this space. I see three options: 1. Wall off now and just deal with all the construction traffic through the master BR to bath doorway. 2. Wait until the last possible minute to build the wall, leaving it open for easier access and less disruption through the bedroom. 3. Erect the wall but leave an opening that is later plugged. Overall, I was thinking #3 but it just seems ridiculous to create a temporary opening (but I have a really good sheetrock/plaster guy who works miracles). Also, we're not dealing with any carpeting (all hardwood floors) and there wouldn't be any electrical or plumbing in the temporary doorway to deal with). Hopefully I explained that well enough; any suggestions? Thanks, BB