10 points for the snark! 
For “casing” (above) see Casing - definition of casing by The Free Dictionary (def. 1)
I’ve used the term before at Faire. Rather than saying someone is late because they had a flat tire, you can say that Lady Darby will be with us later as her horse has thrown a shoe on the King’s Road and she is waiting for someone to assist her.
I’ve heard it as well, and in that context (not a projector, mind you - but something that wasn’t a horse). Raised in Kansas, live in Indiana - not a ton of horses around, but I’ve heard it and probably used it at some point. Most people who’ve seen Back to the Future III have at least heard it used literally.
The weird thing is yes, I also have the act of a horse losing a shoe when I use it, but, I have never owned or known anyone who has owned horses. I’ve only ridden a horse once, and never watch horse racing.
It’s good to see that I didn’t completely make it up, though. Usually looking or phrases on Google produces relevant hits. This time, all I found was Bush stuff.
I’ve heard it and used it all my life and I’ve never had horses. A slightly updated varient would be “throw a rod”.
I honestly can’t tell you whether I’ve heard the phrase “threw a shoe” before—I probably have, but I couldn’t tell you when or where—but I knew what you meant when I saw the thread title, and I thought of it as an old-fashioned-er version of “throwing a rod.”
It’s still possible in some areas to see horse-drawn vehicles on the roads. We’ve got Amish people here in southern Maryland, so I see their horse-drawn carriages pretty regularly - they’re at the local farmers’ market every week, selling bread and pies and preserves and produce.
I’ve heard it, but only in the literal sense, and only from fantasy/medieval fiction.
That really hurt! I’m gonna have a lump there, you idiot! Who throws a shoe? Honestly! You fight like a woman!
Of course I’ve heard it when hanging around horses. I don’t think I’ve ever heard it used as a metaphor, but no reason it couldn’t be. After all, sports people talk all the time about how “the wheels fell off”…pretty much the same thing here.
However, when I saw the thread title, what I thought of was that guy who insulted Bush by throwing a shoe.
I suppose I’m obligated to post. 
I’ve heard the phrase, but I know a stupidly high number of old-timey phrases that refer to phenomena that whippersnappers these days aren’t familiar with. “Heading them off at the pass” is another that comes to mind. Who herds through passes anymore?
Obligatory: get offa my lawn.
- purplehorseshoe, who’s 30 going on 74
Obligatory link to relevant scene from the Blues Brothers.
(Warning: eff bomb included in YouTube clip).
I’ve heard it, but only in an old song about Santa’s reindeer. (Blitzen threw a shoe one Christmas over Mexico, so the ferrier gave him a donkey named Jose as a loaner. Worked just fine)
I really don’t remember for sure if I’ve heard the phrase used figuratively or not. It seems like I may have.
I know what it means and wouldn’t think twice if I heard it used as you did.
We generally say “the fly rod’s gone askew of the treadle” in a very bad MP accent for that sort of situation.
Actually, I’ve known farriers who shod oxen. It depends on what they’re doing and what surface they’ll be on. It’s a bit tricky, shoeing cloven hooves, but it can be done.
Throwing a shoe is a problem for any horse that’s actively working, not just in a race. Horse racing may be the context most people are familiar with, but anyone who is around horses much would know this phrase.
FWIW, race plates are generally much lighter than normal shoes and are put on just for the race. Changing shoes that often can sometimes cause problems with shoes coming off, so it is probably more common for racehorses to throw shoes than it is for the general horse population. However, weighted shoes aren’t that common in racing, although they’re used a lot in some other sports.
I’ve heard it used only in the somewhat literal sense of a horse actually losing a shoe, but I would have inferred your metaphorical meaning.
Here’s a little more [PDF] on shoe throwing concerning weddings. And supposedly this is the origin for tying shoes (I always thought it was cans) on the back of a newlywed’s vehicle.
I’ve heard it, and I know what it means. I’ve even heard it used metaphorically to describe a flat tire. But I wouldn’t think it a very apt metaphor for a broken projector, unless perhaps the projector was broken due to a problem with one its supports.
I have heard this in the context of a person who is unable to work, and instead benefits from a few days off - like a sort of unexpected bonus.
I don’t think this is a cowboy specific thing at all, you have to remeber that horses have been used as draugh animals the world over, no reason it should be a US centric thing at all, a good few US folk seem to think other phrases such as ‘son of a gun’ have a US origin - when it has a Royal Navy origin
I’m that way too. I always attributed it to having parents who were older than those of most of my peers. My dad is 62, mom is 64, and I’m 28.
Grew up hearing and using all of these as well as the ‘threw a shoe’ thing. I’d think of a lost horse shoe long before that business with Bush came to mind.
Same as ‘came uncranked’ is/was ‘the fire went out’ especially when speaking of a super-charged engine.
I myself grew up in West Texas and cannot recall ever hearing the phrase in general use. Referring to horses, yes, but even then only in movies and books, as I was not a horse person and thus did not hang around cowboys.