White mold is very common in new vivariums. It will run its course with or without springtails present.

The types of wood you want to avoid is "GrapeVine wood" (it will get a very nasty grey mold that is VERY bad) and Softwood (think Pine). Hardwoods are great. They resist breakdown and mold. Hardwoods will last a long time in a vivarium in very humid conditions.

Moss from your backyard will most likely die in a humid terrarium. It is work a shot, but typically it doesn't go well.