The effect of freezing on the drying/dryness of wood is a bit complicated. There's a few hiccoughs that make it hard too call exact effects from the theory, at least at my level of knowledge.
What happens is roughly as follows:
If your shop was full of air at 80% RH and at say 55 deg F (typical mildly heated winter conditions) then dropping it to below 40 deg F would result in saturation or 100% RH. i.e the ability of the air to hold moisture becomes less than the amount of moisture present (the dew point is reached), and the resulting dew/fog/free moisture would quite quickly wet the wood. If this condition was maintained the EMC (equilibrium moisture content) of the wood would over time reach the fibre saturation point which is around 30%.
Keep on chilling the air down and you get more and more of the moisture in the air coming out as dew, but the same broad situation pertains.
Once you get below freezing/the triple point/the frost point the dew starts to drop out directly as frost. Once below this water can no longer be present in liquid form, and your wood cannot take up any more moisture.
I don't know the psychrometrics exactly (it's about maintaining the right partial pressures), but if say you were to bring that piece of frozen wood indoors into a warm room at low RH (the likely result of heating frozen air taken in from outside that does not by definition contain a lot of moisture) you would likely get sublimation or freeze drying of the wood - the frozen water in it would convert invisibly to water vapour, mix with the air passing through the room and be taken away. i.e. your wood would dry out, but how quickly i don't know. The rate of drying would fairly quickly slow down (once the wood had warmed up, the ice melted, and its sublimation consequently stopped),but the wood would as you would expect eventually air dry as normal down to a very low moisture content.
So it's a bit of a swings and roundabouts deal depending on not just the exact conditions, but also on how long the wood is exposed to them.
On the face of it though periods spent at temperatures just above freezing/around the dew point are likely to result in what could be quite large increases in moisture content - but i don't know how fast wood takes up moisture in saturated air. It'll be the worst case (fastest possible) situation for moisture gain though.
Once frozen the situation is pretty much stable (no moisture can be taken up as its locked into ice), but held for long enough in the right conditions then warming (while staying below the frost point) should result in the loss of quite a lot of moisture by sublimation. (the frost converts directly to water vapour in the air, but without becoming liquid on the way through)
If it stalled slightly above freezing again on the way up, then you would probably (depends on the room conditions, but presuming the same air/moisture content you started with) be back into saturated (dew filled) air, and back to the rapid take up of moisture.
On the other hand a quick zap from normal conditions down to freezing, followed by a rapid return to normal conditions when the freeze ends would likely have very little nett effect.
I do know there has been work done on the freeze drying of wood in naturally occurring Winter/Spring conditions in Northern Canada.
As long as the wood is not 'green' (it's below the fibre saturation point or ~30% MC, so that the cells contain no liquid water, and all moisture is contained in the cell walls) freezing apparently does it no harm....
ian
