If the hose/wire is encircling the whole trunk, you will do more damage chipping away the bark to remove it now. First, I would see if you can pull the hose/wire out just by grabbing on the part sticking out (using pliers for a firm grip) and peel/pull it away from the trunk. Looks like the other trunk has the same situation. You can see that the tree is trying to grow around the hose/wire with those swollen growths. The growths will eventually grow together around the hose/wire and enable the tree to survive the trauma. Remember that the actual live part of the tree bark is only a few cell layers thick (phloem and xylem layers... remember high school biology?). If they are cut through around most of the tree trunk, the tree is toast. Most likely, since the tree is still alive, those living layers are just behind the hose/wire. If you can gently pull/peel the hose/wire away from the trunks (kinda like opening the safety seal ring on a bottle or milk jug), you will allow the tree to revert to normal growth. The latest research says to NOT seal the wound with anything at all, which would hinder healing naturally.
I had to do this to six trees that I happened upon at a fast food place a few years back. The original staking systems had never been removed and the trees (red maples and hawthorns) looked exactly like your situation. When I alerted the store manager and showed him the trees telling him they would most likely be strangled in another year or so, he said to go ahead and do my best to take care of it. I was able to "peel" the hose/wires off the trunks with varying degrees of success. While most of the trunks were freed of their wires, on a few trunks, I could get just most of the hose/wire removed, and there were a couple where most of it was too far ingrown on the trunks. Three years later, they have all survived and even the ones with most of the wire left on seem to have grown around the wire and are doing fine, probably because the hose part had pretty much disintegrated in time to not be a factor and the tree grew around the wire. Another year or so and I'll know for sure.
However, many years ago, one of my crew left plastic wrapping cord on at the base of a balled and burlapped blue spruce. A few years later, in late spring, the tree turned completely brown and died within a week. I discovered the problem when digging it out. I think it didn't stand a chance since there were four or five windings of thick twine around the trunk. It had made a valiant effort to grow around the twine with considerable trunk swelling beneath the wrappings, but it was not to be. Your trunks have a better chance with just the one to deal with. (By the way, I replaced that spruce at no charge, being honest about my error ...actually that of an employee, but...)
Good luck. Let us know how it works out.
