#1 but with a door moved so you face the vanity when you walk in or #4

So you have to go outside to access the facilities? I guess it’s not an option to punch a hole in the existing side wall (hence your comment about doors not being cheap . . .)?

Punching through would require an interior rethinking, moving built-ins and equipment. Outside also gives option to use without unlocking barn for people camping nearby. In general, it's really an indoor/outdoor area already.

Ah. ”people camping nearby.”

Is this in an area where freezing temperatures occur?

Yes, freezing November to March or so. Water already at barn that gets winterized. Of course accomodations will be made. Interior wet wall will help a little but the barn is only occasionally heated.

If you are going to the trouble and expense of adding a toilet, hand sink and utility sink, consider adding a floor drain also.  Add a shower wand to the utility sink and you could hose down a dog, dirty feet, messy toddler etc.

Will this be a cold-water-only room? If not, will the water heater be inside the barn or outside in the powder room? On-demand or tank storage? Will the summer campers want showers, too?

apple_pie_order There will be an on-demand water heater. It will likely be one of the small electric on-demand styles. Campers and showers - They say no. Also, camping will only be a once or twice a year thing. I'm kicking around a shower but I doubt it will ever get used much. The primary use case for this bathroom is to avoid using the woods or driving/walking to the house a quarter mile up a hill. Secondarily, as a place to wash dirty/greasy hands or clean paint brushes or whatever.