Wire 'marking' the bark is most commonly because it was left on while the stem thickened (during the growing season). It is often referred to as the wire 'biting in', but it is because the stem thickened.
At any rate, this won't happen during dormancy, simply because there is no thickening or lengthening growth. There can be processes still occurring that make the stem 'lignify'. Once it has, the wire can be removed. During the growing season this takes just a few weeks.
I judge whether the wire can be removed by gently unwiring the end of the stem and seeing if it holds position. If so, the wire can come off. If not, I gently rewind it back like it was. Rinse & repeat.
Over the winter, dirt may accumulate near the wire or the wire may react with something (possibly exuded from the bark) and leave a residue 'marking'. These should either scrub off with a toothbrush or will disappear as the bark ages (one can paint the bark to mark a tree, say, and after a year or two it wears away).