Cooled Cabinet Humidor Project

Don't over analyze the moisture issue and make it worse.
To better understand the issue, here is an excerpt from the Dept. of energy consumer’s guide on foam board;

"In cold weather, warm inside air containing water vapor can get past the wall finish and insulation, condensing inside the colder wall cavity. In hot, humid climates the same thing can happen, just in the reverse direction. Humid outdoor air in the summer can condense inside cool, air conditioned wall cavities. If enough of this happens and the water cannot escape, wood rot, mold, and other moisture-related problems can occur. For this reason, building codes often require installing a vapor diffusion retarder on the warmest side of the wall cavity."

The keys to your project, if installing a vapor barrier is to determine;

• What is the warmest side of the box?
• Will there be airspace between the 2 units?
• Will there be adequate places for the moisture to escape on its own?

You can make it worse if you trap it in a void and it cannot escape.
Also check with the supplier where you buy the foam,
some already contain a plastic coating that will act as a barrier.
I would just place that side against the cedar side of the cabinet and let the rest of the cabinet breath to keep from rotting.

Keep in mind the concern with moisture in this application is not the amount of moisture in the cabinet vs. outside (cedar will do most of the work containing it if installed properly) it's the temperature difference inside vs. outside where condensation will be created.

In most case unless its in an extreme location it's not going to be a problem.

Chas