Turn them upside down. There's probably a mass of roots that pretty much fills the pot. If you didn't have them set on something there might be roots going into the ground. BUT...if it's a tree you want, and since you've removed all the top growth, just let them sprout out and remove ALL the sprouts in each pot but one. Train that single stem to a trunk for 4-5 feet and then let it branch out.

Obviously willows are very vigorous & would probably survive a nuclear explosion, so that might be an option. Seriously though - it would have been better to wait until spring to tackle this project. Chop the root mass into manageable sections so the old soil CAN be removed & repot into a suitable soil. Doing it now means the plant will expend all or nearly all of its stored energy to push a new flush of foliage, which won't have enough time before freezing to pay down the energy invested. Had the work been undertaken in spring, there would have been no danger of the foliage freezing & you would have had the entire summer & fall for the plant to rebuild its energy reserves.

Willow wood is soft, so it's possible that the soil might have hardened to the degree it's actually harder than the wood. I've seen this in mugo pines & other nursery stock that was continually bumped up, and it's not easy to deal with. Your options are pretty much water under high pressure and various tools used in mechanical removal.

Good luck - dividing or starting new plants from cuttings seem the most reasonable pursuits to me.

Al

I am not trying to restart these willows. Au contraire...I never want to see them again. I just want to get the compacted soil out of these huge containers so I can use them to plant other trees. The last thing I want to see is the indestructible willow tree start over again.

Turning them upside down is not an option. The soil doesn't move and the barrels with the soil must weigh close to 300 lbs. They're big. I am not sure if water will help or hinder the process...making the dirt expand.
I was going to try to cut into the soil with the sawsall
but it's much harder than I imagined. It's like concrete
and the saw just bounces off the soil. I don't know how high pressure water would help get it out of the container,
but I don't have access to high pressure water anyway.
This is a roof garden and the water pressure is pathetic up there.
Would the soil eventually break down if I just left it sitting in the barrel and not allow anything to grow?
Is there something I can pour over it that would break down
the root system and prevent new growth?

You can try Stump Out.

wow, just read about stump out. thanks for the tip.
Will try as last resort since you have to wait 6 to 8 weeks
before it is effective. However I couldn't light it on fire, as suggested, since we have fire regulations prohibiting fires on roofs in my area.