I would always fold the wirw like you fold up an electrical cord wraping the last of it around it's self and store it in an empty feed sack. There are tons of uses for bailing wire. I didn't know they still used the wire. I even made a garden fence out of bailing wire when I was younger and could not afford the wire for the garden. On the race track they would make emergency harness repairs with bailing wire and electrical tape.
I use the twine, not the cheap kind I like the orange or black stuff, I take 3 and braid it together knot the ends and use them to make handles for the muck buckets, what I do is figure how much I need and knot it with two knots close together then cut in between the knots, braided it is triple strong, I have made a temp gate with them, tied gates on for a temp enclosure, make a loop to secure a gate to pull over the post, got some of them still in use for years now, tie water buckets to the fence, keep a braided one in the car just in case you see a loose horse or dog.
Lots of uses, if you have the twine that is not the plastic or what ever that orange stuff is made of you can do the same thing for temp use, it just dont last as long.
hope that give you some ideas, another thing I do is hang horse toys from the cieling, I tie braided twine on toys to they have something to grab on to when they play, those horse balls have to thick a handle for Mini mouths, or you can use them to tie to a baby halter for a grap strap.
I am sure people can think of more, those are just a few things to do with twine.