Have fun looking at this word, and then have fun saying it.
If it snags your eyes, it’s with good reason: the second half of it is just the first half rearranged… in the spelling, that is. The pronunciation is almost completely different – /r/ is the only phoneme the two halves have in common, and it’s a mere glide in the first half and a full syllable in the second.
In the first half, the o is made with the tongue lower than with, say, over, and higher than with, say, on. The s is voiceless, as indicated by the e, which is not pronounced and is just there to keep the word looking like a plural of hor and having the s said [z] – originally there was no e written on horse.
In the second half, neither s nor h is said with individual value; although we have, and have always had, the “sh” sound in English, classical Latin didn’t have the sound, and so our alphabet didn’t come with a symbol for it. In Old English it was written sc; now it’s sh. The o has always been there in this word, and used to be said [o]; the e has not always been there, though in shoer it would be there anyway as part of the er suffix. And again the e is not said; we just go straight to the r (if you’re British and glide the r, you’re still not saying the e as you would if giving it normal value; you’re saying a sound reserved for er, farther back in the mouth).
If you’re just learning English, you may well think that this word was invented by the devil, or at any rate, its referent notwithstanding, that it is quite unlucky. It stands as evidence against the silly assertion that English is a logical language. It also forces you to make a sound remarkably like that of a dishwasher in action (and nothing at all like the clank of a horseshoe). But, better still, it forces the speaker to do something rather unusual: follow an alveolar fricative with an alveopalatal fricative – you start with that [s] and then immediately have to slide the tongue back a little off the ridge. It’s just screaming for the first sound to be assimilated into the second. And it probably would come to be thus if it were a common word.
Now, it is made of two common words, both great old Anglo-Saxon words emerging from the mists of time little altered. And its referent is nothing new – someone who makes horseshoes or shoes horses. But even though there is still work (if less of it) for such tradespeople, they are not commonly called by the plain (if horse-whispering) word we have here. No, fittingly for a line of work that persists mainly in rather upscale milieux, it gets a Latinate denomination: farrier.