(I’m sure right about now someone will post a photo of a well-used Winkler to prove me wrong.

I’m sure
someone is using their Winkler.)
OK, I'll bite

Guess it's time to remedy the absence of photos of a user-Winkler.
Winkler Camp Axe, TAD Edition (early version w. tapered tang) by
Timichango, on Flickr
Winkler Camp Axe, TAD Edition (early version w. tapered tang) – Verso by
Timichango, on Flickr
Had this puppy since 2016, and it was as-new when I bought it 2nd hand (never used, sharpened, scuffed, etc.) Pretty quickly after laying hands on it, I wound up re-profiling the edge to convex, as I wasn't ecstatic with how obtuse the stock bevel was, nor the noticeable lopsidedness of that bevel. The stock edge was plenty sharp, mind you, just not acute enough for my preferences and uses. I do generally prefer a convex edge on an axe if for no other reason than that it simplifies my life a bit with regards to sharpening, as I can use the same equipment as with my other axes (a couple of Gransfors axes).
The photos shown here represent about two dozen nights' worth of camping & campfire wood prep: busting down purchased firewood into kindling, making feather sticks (it'll do it, but it's obviously not the ideal tool for that), limbing or taking down smaller standing dead wood for scavenging firewood, chopping/shaping tarp pegs/poles, some food prep (busted down a handful of chickens with it, cubed out some chuck for stew, chopped assorted veggies, obliterated some pumpkins, used the side of the head to mash many cloves of garlic, etc.), used the hammer poll to beat on a lug wrench to get a stubborn lug nut to budge once, and — maybe the most unexpected use I've applied it to — used it to shear sections of 4AWG copper wire when I was making up new battery cables for my update of the auxiliary electrical system in my van last year: couldn't find my chisel, and the axe was on-hand in the garage, along with a big stump I'd been using to pre-prep firewood for impromptu bonfires at the river across the street. Decided to try a test cut with the axe, and it was laughably easy to get through the cable in a single stroke. Second cut on each of the two leads I was making up was measured out, and then the winkler pounded through the cable with a urethane dead-blow hammer, for accuracy (still working on developing the accuracy of my axe swing...).
Anyways — that's what it's been up to since I got it, and the wear shown is the result. Not too bad. I'm more or less indifferent about coatings anyways, having owned other carbon steel blades for years, and never having had a stainless axe or hatchet. That said, it is pretty impressive that it's still mostly coated — only the first inch or so of the head behind the edge has any significant wear, and the rest of the mottling you see (other than the obvious directional scuffs) is mostly just discoloration of the coating from contact with food, finger oils, whatever.
For someone who might be more concerned about maintaining some kind of coating after use, I *did* do some searching around the internet soon after I got the thing (and before I decided I really didn't care), and found this:
https://www.caswellcanada.ca/black-oxide-kit.html — reckon that's what you'd need to re-Caswell the thing. For my purposes, a lightly mineral-oiled bit of cotton shop rag kept on-hand in a small ziploc does just fine.
One thing particular to the Winkler axe and its (fantastic) sheath: the felt-lined kydex has had two main downsides, for me, in my somewhat limited experience: the felt is pretty good at trapping moisture and/or grit, if it's exposed to either. If you're particularly concerned about corrosion, then keeping the sheath off the ground is a good plan for minimizing grit—your belt's a pretty good place for it, but if you're using around camp and sitting down a bunch, then that can be a pain, and all of the times I've dropped it in the dirt/sand have been when I'm loafing around a campsite. Moisture's bound to happen at some point, so even with the coating intact, you're going to need to oil it to keep the edge itself from rusting. And if the sheath felt ever gets really wet, you'll want to get the axe out of it and let it dry when your trip is done, since it won't drip-dry like a plain kydex sheath will when the head is in there — seems to need a bit of airflow in there to dry out if it's a smidge soaked. Doesn't take too long, and the lining seems to release moisture pretty well with a bit of pressure, so an absorbent microfiber cloth or some decent paper towels can help that process along nicely. In practice, though, even with some mildly negligent episodes in my own care and feeding of the thing in inclement weather, the thing doesn't seem to be in a huge rush to oxidize — had some superficial rust spotting around the edge when I lazily stored it in a damp (and gritty!) sheath one night after a touch too much bourbon with an old friend I was catching up with, the superficial rust got worn off handily by simply processing some kindling to get the morning fire going for some badly-needed coffee. Seemed to fare better than my old Bark River Gunny (in A2 steel) being wet overnight, despite my impression that A2 is more corrosion resistant than 5160 (what this generation of the axe was made with). Makes me think that even though it's pretty faint at this point, the residual oxides from the worn coating behind the edge are still helping out with the elements.
My normal touch-up routine on the Winkler after a few trips' use (or whenever it becomes noticeably less keen) is a gentle & fast circular pass with the fine side of the Gransfors Bruks ceramic puck to bring the edge back, and then a quick strop on a paddle loaded with a couple different grits of CBN emulsion (2000/4000 on opposite sides) to polish it out a bit. If I'm at home, and not out camping somewhere, I might do a quick pass between the puck and the strop by hand, using the fine/ultrafine rods from a sharpmaker, running in a circular motion much the same as with the puck, just to bridge the grit gap between the puck and strop and speed things up a bit, since the jump from the puck to the 2000 grit side of the strop is substantial.
I've also simply sharpened it up on a 4" x 3" chunk of 6mm thick neoprene, harvested from a defunct wetsuit, with a piece of 1000 grit wet/dry norton sandpaper over it — that's what I've got snugged into my little firestarting kit along with my other bits and bobs, and it's what I pocket if I'm cycling or walking to wherever I'm camping (or just doing an evening fire down by the river).
Anyways, that's a lot of blather from me about the axe, when the reality is that it's a super robust piece of kit, and coating or no coating you'd need to be seriously negligent for a serious amount of time to meaningfully damage it that way, beyond cosmetically. And they look better used anyhow
