I am building a wine cellar, we have 3 1/2" of closed foam insulation. One wine cellar company says that I do NOT need a vapor barrier because a double barrier is a recipe for condensation and mold disaster in a few years, the other one says I do need an additional vapor barrier because of the humidity in Texas.
Closed-cell foam insulation is a vapor barrier itself. If this closed-cell foam is continuous, then you shouldn't have any issues. If it is just in the cavities between wood studs, then the studs may act as thermal bridges which may result in condensation on the humid side if the studs get cold enough.
wine cellars are special creatures because they have their own temperature and humdity control systems. its further complicated by the fact that where you are and your local climate change how you build them (in modern homes anyway)
in most homes or buildings, the desire is to keep the cold dry air out and the warm humid air in. thus the need for the vapour barrier inside the wall (on the warm, humid side of the wall).
however, in a wine cellar, it can sometimes be cold and dry on the inside of the room (compared to the outside conditions). in a place thats very humid, you can get the exact opposite effect where condensation builds up on the room side of the vapour barrier, which does create problems.
the traditional way to solve this was not to. the stone walls of the wine cellar didnt care if they got wet. they were stone. however, nowadays, we have less stone and more man made materials.
the simplest fix is just encapsulate the foam inside and out with an air barrier (tyvek or typar will both work). this will let the wall breathe, ensuring the wall, if moist inside, can dry out. less energy efficient, but the best choice in a climate like texas. just make sure you install it in the correct orientation. you want the permeance direction to always be out from the inside of the wall (so it goes one way, usually writing side out, on the outside of the wall, and the other way, writing side in on the inside of the wall)
you should also use cement board and tile or stone, or slats of wood as your interior finish, because the former isn't bothered by humidity and the latter can breathe in order to dry out the inside of the wall.