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It's not just the American army.....
The British army had adopted a spiked hemet as 'standard' dress for line infantry regiments in the late 19th century (ie: around 1890), for example....
Which, incidentally, made/makes it relatively easy using the 'old' (and really excellent) Airfix WW1 German infantry set, to model something that looked/looks like British infantry circa 1890...if you were/are that way inclined.
I apologize that the links won't work, but I saw the prints in a book about the US army and all its battles and operations in the old west. It's titled something like "Old West: The Soldiers." That is an interesting idea though Mike. I'll have to add that to a list of future projects. Also as you mention Minuteman it wasn't just the Americans. After doing some more research I've found that many South American countries adopted a pickelhaube style of helmet as well, some of which still use it today for ceremonial purposes.
Here is one link showing U.S. Cavalry (Buffalo Soldiers) on parade at Fort Davis, Texas 1875. Make sure you click on the little squares at the bottom of one of them to see all the photos. There is a great dismounted, group, close-up photo:
Here is another link, Wikipedia, so just scroll down to the middle and you'll see a nice illustration showing the same:
I would call these helmets Sun Helmets made of pressed felt or cork. Pickelhaubes were made of leather, and typically as we think of them in the German Army of WWI, had a much lower top fitting closely to the head. The Russians did have them taller during the Crimean War. Strelets makes these Infantry and Cavalry sets. These (I believe) would be made of leather:
U.S. Cavalry during the Indian Wars quickly adopted the Slouch Hat, like Strelet's Wild West set for field duty. The british mostly swapped-out the tall spike for an air vent for their Foreign Service Helmet or Pith Helmet or Sun Helmet. Hat covers these helmets in their Zulu Wars range pretty well, but none have the spike even though some Carabiners did leave the spike.
Bottom line, I think the U.S. Cavalry adopted the cork pith helmets similar to the British. The Pickelhaube was worn by the Russians (in a tall design of leather - Strelets) in the Crimea, Germans in the low design during WWI (Airfix), and also as you mention South America.
Have fun with any conversions you do and be sure to share them!