I have one, a Sony Z3. I like it, partly because it's water-proof and partly because its batteries last me several days, but it's not easy to use with conventional gloves on.

A quick and dirty solution is to put the phone in a "hefty" type resealable bag. The touch screen on my phone (Samsung G-6) works through the bag, and the bag is waterproof.

Exactly. There are cheap bags exactly for that widely available, as well as waterproof cases, as well as warm gloves, to work with touch screens (in cold weather I'm wearing wool mittens converting to cut off fingers gloves, tested ideal down to 0F).

My smartphone is waterproof - but forget about working the touchscreen when it's wet. Doesn't work, at least not with my fingers.

I actually think one of those (semi-)waterproof smartphone pouches where you can use the touchscreen through some kind of transparent (plastic?) material would work much better in precipitation, at least when it's not too cold outside. Those pouches might get very stiff when it gets cold (untested by me).

And don't forget -- when it's bad I want to use the unit with thick gloves or mittens. Then I want big fat buttons to push!

Can you tell, what exactly needs to be controlled on a GPS by these buttons? (Itemized list, please).

During transit: No bare hands-operation
Zoom in / out
Pan
Toggle between different modes of navigation display (map - arrow showing direction to next waypoint, )
Set wp at my position (and preferably give it a name that makes sense)
show/hide my track

Preparing transit: (Preferably done somewhere quiet, where I can consentrate. Normally, I'd do this stuff with bare hands).
Prepare waypoints (from coordinates, or by clicking in the map)
Map display - to familiarize with route, and how the GPS map will display the terrain.

Thanks.

I can suggest the following:

1. Zoom in / out - 2 volume buttons, they are large enough (alternatively, shake the phone up/down/up/down to zoom in, down/up/down/up to zoom out - the first move dictates the direction, others - confirms it);

2. Pan - tilt the phone for more than 45 deg to the direction you want to pan, then back to normal for a fixed pan step;

3. Toggle between different modes of navigation display (map - arrow showing direction to next waypoint, ) - Shake your phone vigorously left-right (along the short side) to switch the mode from the looped list;

4. Set wp at my position (and preferably give it a name that makes sense) - cover the top of the screen with your hand (glove/mitten/bare/your forehead - doesn't matter) to trip the proximity sensor and cause the WP registered on the map (optionally use the voice to input the WP name, or I can think of gravity driven keyboard if you so prefer - still better than the 5 buttons input of Magellan);

5. show/hide my track - shake the phone forward/backward (along the longer side).

Also we have in the reserve "turn the screen over (screen down) and back" and "slap it with other hand at one of its 6 sides N times" but these are less practical.

Would that work for you?

I have my doubts - but I wont make my prejudices stand in the way of innovation! If you make it, I'll try it!

Operating the volume buttons works OK on my device with my mittens and my fingers. I can't feel it - but I just push where it's supposed to be, and that works.

You should also know that I'm not interested in holding my navigation device in my hand perpetually when moving about. It's tiresome, and it's just too easy to loose it. So my device will be tied to a loop over my neck and one shoulder. It is super easy to grab it with one hand, operate it and just let it dangle when I've satisfied my navigation needs. That could possibly create caos in your "turn the screen over" logic. Or perhaps one of the buttons (the volume?) will take the device out of "screen saving mode" into "operations mode"? And some flick (or dropping it 4 inches, then dangle) would turn off the screen and all operations?

Yes, I understand your concerns. Sure thing, prior to "shaking" operations the navigator must be brought into the "operations" mode. Is the regular "Power" button is too awkward to use? Both of mine are superb. I like the "dangling" command idea. The screen off mode trigger could be configured simply for a certain device orientation (like the vertical one, on the lanyard). I can rig an app for proof of concept testing soon, however at the moment I'm working with the Google Maps API, which might be not good for a serious testing in the field, as it requires an Internet connection (no caching is possible with their API). However, I plan to switch to the OSM at some point, as it looks robust enough already, with many hiking trails mapped by the community. I doubt I'm going to compete with the plethora of Android NAV aps, but the OSM community may listen to this idea and add such a feature to my favorite OSMAnd project, for example.

By the way, when hiking I'm carrying my smartphone on the neck as well (not sure what you mean about the shoulder though, under the armpit probably?). The lanyard is long enough to operate the device, as well as to put it into the shirt's front pocket, when dangling is inconvenient (i.e. when climbing a rock), or a bit more protection required (i.e. dust).

Also I have invented another technique for the convenient phone lanyard, which does not require a loop, thus not require a breakout device for it either. With that, the phone is riding high (just below the shoulder line) on the one side of the chest (pectoral), the lanyard goes up over the shoulder, behind the neck, over the other shoulder and the other side of the chest, and connects to the shirt's button hole or to the collar of the T-shirt (with a pin/clamp/-binner). That position is much more safe and convenient for carrying the phone ready for action, as it's not actually "dangling" much when your torso moves. You can easily glance at the chest's side to see some info quickly, or pulling the screen a bit, as well as operate it to some extent, and you can always move it over the neck and bring in front of you for more extensive operation. It's is still short enough to stop the phone's falling from your hands far from the ground. In fact, my phone's lanyard is a 5 "strands" folding transformer with an S-binner and a ring, which allows the neck, wrist, shoulder, belt, and even single finger carrying/holding I should make a post about it some day.

A traditional paper map is easily handled while walking, and the hand maneuvers are fairly intuitive and not very complex. I suppose this is what an old geezer who has been handling paper maps for over fifty years without becoming hopelessly lost might say....