Overwintering trees in containers

I'm growing a lot of trees out in root pruning containers this year.  Most I will use myself and put in the ground this fall, but since fall is when the most root growth occurs, I would like to leave some in the containers to grow bigger root masses to plant the following year, as well as to pass on to family members and friends.  My question is, how do I best overwinter the trees in containers?  Our winters get very cold, and freezing them solid seems unwise.  I don't know if piling a foot of wood chips over them would help.  My woodchip piles freeze solid in the winter.  I could plant them and then dig them up again in the spring and put them back in containers, but that seems like a silly waste of time.  Anyone have any insight into the best way to do this?  Please keep in mind our weather that almost always hits -20F, sometime hits -30F, and one year hit -40F two nights in a row.

I don't know a very cold climate so I can only talk to what we do.

We get a lot of freeze and thaw (sometimes two or more times a day).  It seems that (many) trees don't mind their roots freezing. In some parts of the world, it does that in the ground and there is this thing called a "frost line" or something.  It's the rapid freeze and thaw thing that gets them.  

The best way I've found for keeping trees in containers over winter is to burry the containers in the garden.  That way the roots are slower to freeze or thaw and we have as high a success rate in the pots as we do in the ground.  The only big challenge is not to burry them too deep or on an angle.  About the same level as the soil in the pot seems to be best.  

It seems to me that your idea of putting wood mulch over your root pruning box would work great!  Especially, perhaps, if you temporarily covered the non-tree areas first with plastic or landscape cloth simply to make removal easier in the spring.  If you did all this right after they went dormant, I think root pruning wouldn't be an issue over the winter, the plastic & wood chips all around the edges would keep the breeze out from beneath and protect the whole bunch from drying out & extra cold, and the uncovered top part where all the trunks were would be open to receiving all the healthy rain & snow.  Without tunnels underneath the roots to make them colder and drier, anything you were growing that was already hardy to your zone I think would be completely fine even when the pile did freeze... since they are made to handle that much already, just fine.

Make sense to you?  

I think the greenhouses around here (very cold climate) wrap the root ball in burlap, bury it in the ground and water it well before freeze-up.

Perhaps they could stay in plastic pots, but they don't breathe. Too much or too little moisture could be a killer. I suspect some contact with the broader soil keeps the roots healthy.