I would definitely use a vapor barrier if you do build a separate room, as the main goal will be to have the room sealed well, , to allow things to have the best chance at staying a certain temp, humidity
I worked in a clean room(15+yrs) that was both temp and humidity controlled to never change temp by mroe than 2 degree's, not to mention had to be almost 100% dust free too!
to do so, we had to have a separate entrance before entering the main room, the walls were some sort of Plastic PVC type material,and all seams were sealed that or some walls were complete solid glass, (12ft+tall and in I think 6 or maybe even 8 ft wide sheets been a long time since had that job) and had exhaust and AC/heat ducts in ceiling!, concrete floor coating with some anti slip coating, once things were up and running, things stayed the same temp pretty darn close,
but when ever you opened a door to get in, even with the second entrance way deal, there was huge vacuum like air movement , it came and went fast though!
Now I am sure you don;t need things that extreme, just giving you an example of what I experienced! and some idea's maybe!
and I 100% agree a ton of timber you get from stores anymore already has mold on it, and just cause you don;t see , doesn;t mean its not there, mold is on many things long before it turns green or black/white1
if I was going to build a temp controlled room, I think I would pre treat all things before sealing them up!, they sell spray solutions you can treat things, not super cheap , nor super costly, just would add a layer of less concern for me!
now another thought for you, to maybe consider
have you thought about building a covered like car port<
you can maybe pour a concrete perimeter around it, add some thinner wire mesh , or even perforated metal sheets into concrete and as walls to keep mice out,, just get things with holes small enough to prevent them from fitting! if you go with perforated metal sheets, be them aluminum or steel, you can always paint them to make it more enjoyable on the eye's!
fill center of pad in with gravel inside the fenced in section, if you follow,
add a good sealed garage door to one end, and then you would have it outside to get good air flow, yet still have a critter proof set up,
if you build it wide enough and with enough over hang on sides, it will keep pretty much all snow and rain out!
yet again allow you all the free flowing air and just be stuck with what ever humidity is about< no control over that, but might be a less costly option than building an enclosed temp/humidity controlled environment deal!
food for thought??