Does the lid make it airtight? If not, it's OK, the soil needs to respire.

i would doubt the side insulation was necessary .... dormant is dormant ...

the top should be baited in case of rodents ..

they key ..as with all potted plants ... no matter what plant.. or what pot ...

get it dormant.. keep it dormant ...

pots can thaw in winter ... especially if left in the sun .. ANYTHING you do .. to insulate from the effects of sun.. or a warm snap.. is positive ...

in the cold zones.. get the soil frozen ... the plant dormant.. and KEEP IT FROZEN and the plant frozen.. and you are all set ... iots the repeated back and forth that is the problem ...

the 4 footer.. probably un-necessary .. the 12 inch deep pot.. probably a good idea ...

as for the top .. there is no reason it need be in contact with the soil.. as long as it deflects any direct sun ... which might avoid the rodent issue ...

i am pretty sure.. van wade covers all his pots with fold-able insulating sheets inside his greenhouses ... and loses about 50% [or some ridiculous % he once told me] .. mostly all to the vermin ...

ken

I don't think the top will cause any harm, but may not have been necessary. I think piling leaves around the side would have been enough...even that may not be required.

"I am hopeful that this will protect the little guys."

I assume you mean the cold, they do not need protection from the cold in Z4 but they do need protection from the dreaded freeze/thaw cycle Ken addresses. And you don't want this space air tight. Leaves on top will allow air movement and help with times when it warms up the freezes.

Van Wade's insulation cloth is to avoid the freeze/thaw problem.

I'm sort of summing up what everyone is saying, probably not necessary.

Lois, I'm a zone 4 and along the south side of the lake so I get the cold north wind blowing through my yard. I have had some problems with a 2' raised bed that has "winter" shade so once it's frozen, it stays frozen! I had some hosta losses one year when my straw/leaf mulch blew off. Now I put down straw/loose leaves and then lay wire fence pieces/ medium size branches/ pieces of snow fence on top of the straw so it won't get blown off and I've had real good luck with that.
Peggy

Thanks, everyone. It was the "dreaded freeze/thaw cycle" that concerned me. I thought the warm spring sun shining on the side of the box might cause the soil to thaw prematurely. The lid concerned me because of varmints or rot. I may just take it off, but if I do, I think I'll put more leaves over the hostas and weigh them down, as Peggy suggested. So far I haven't lost a single "special" hosta since I got bitten by the bug in 2006. I guess that's only two winters, but it's a good start. I do pile extra leaves on Sagae and montana Aureomarginata and then cover them with a wire dome. I also try to keep leaves covering about 25 hosta that are located on a south-facing berm. Because that area is under some evergreens, it doesn't get a lot of snow cover, and the early spring sun can really warm it up. Thanks, again, for your responses.