Where to locate moisture barrier in engineered hardwood floor sandwich placed over insulation board?
I am curious what you consider to be "very very cold". Here in Maine, 45 to 50 degrees at slab level 4 feet below grade is common. So interested in what temps you may have and the average relative humidity in that space.
With those questions asked; the straight answer to your question is yes, you should use a vapor barrier when installing any wood type floor over concrete. Both methods you mentioned would work. A one inch foam insulation, closed cell, waterproof, under the subfloor would be fine. If you use the tongue and grove style and fit it carefully, additional vapor barrier should not be needed. You can add a sheet of 6 mil plastic under the insulation for good measure if you feel the humidity is high in your area and are concerned with condensation. Another option is a paint on barrier such as Hydra-loc or any low pressure concrete coating used for interior waterproofing. Again, use this under your foamboard insulation. The one step method is the interlocking subfloor systems with a built in moisture barrier. this works well but is very pricey.