Is it possible to create a magnet that will affect anything it comes near?

Not as far as I know, though you could add every part of every object in your scene if you are wanted (and Poser didn't crash).

RHaseltine is right, a magnet has to be told what to affect, by default it only affects the element that was selected when the magnet was loaded. You can add other elements to be affected by selecting the magnet and using; Object>Properties>Add element to deform. This can be a laborious task if you have a lot of elements to add. In some circumstances pose files can help to automate the process by injecting a list of deformTarget's. Attached above is the text of a pz2 that should add all body parts of P4 or Mill figure that a magnet is attached to, as elements to deform (I haven't tested this exact file as my computer is bust at the moment, and so I don't have acess to Poser). Save the file with a pz2 extention to a pose pallet. I have not tried using pz2's to add deformTarget's across multiple figures, or to a figure + props, I doubt that it would work unless they all shared a parented relationship.