The first thing you have to get your head around is the idea of a magneto-motive force (mmf). Emf is easy to understand because it exists (usually) between two points. Mmf always exists around a complete loop. There is no start and no end, an idea that confuses many an otherwise competent engineer. If it helps, think of a hundred 1.5V batteries all joined up in a circle. You know you've got 150 volts but there's nowhere to measure it - and if you think you could find 75 volts between diametrically opposite points you'd better think again!
With an electromagnet, the mmf is equal to the current passing through that loop in amps (Ampere's law). Yes, mmf is measured in amps but, to avoid confusion, it is more often given in amp-turns. There is no magnetic difference between a 1000 turn coil carrying one amp and a single turn coil carrying 1000 amps. With a permanent magnet you can't measure the current because it's all inside the atoms but it's still there.
So far so good but now we introduce a magnetic material like an iron horse-shoe magnet into the loop. The fact that the iron is the source of the mmf doesn't change anything. What does change is the way in which that mmf is distributed around the loop. Most of it will appear across the air gap because iron is a very good magnetic 'conductor' (that's real Dummies' talk).
This large mmf between the poles of your horse-shoe magnet tends to demagnetize the thing. Every agitation, whether mechanical or thermal, is likely to lead to some loss of alignment of those magnetic domains. The effect of adding a retaining clip or 'keeper' is to distribute the mmf evenly around the loop. If you could probe around with some magnetic equivalent of a voltmeter you would find virtually no mmf anywhere. There is now very little incentive for agitated domains to move about.
If you haven't quite grasped all this yet here's another conundrum to think about. You can magnetize a soft iron ring by passing some current through the hole in the middle. Now soft iron has a very thin hysteresis curve so it doesn't hold permanent magnetism well and yet you have just made a decent magnet out of the stuff. So where's the catch?
Wrong question - where are the poles? As soon as you break the ring to get at some poles the resulting uneven distribution of mmf wipes out most of the magnetism! If you want proof that the magnetism ever existed in the first place you can wind a coil on your ring. Use this first to magnetize the iron then measure the induced voltage in it when you break the ring.