Yes, the plants can look very sad in the winter, some even black and withered, clearly dead but................ the roots almost always survive.
As soon as the worst frost is past, the broken off and dead ones send up new shoots. They have a headstart because of the rootsystem and we always harvest by the time the spring sown ones just started blooming. Most important, before the black flies.
A nice extra benefit is that after the broadbean harvest there is plenty of time for another summer crop in the same space.