IKWYM, I used to have an HTC Legend and I soon learned to keep the GPS
*receiver* turned off when not in use. But I'm pleased to report that the iPhone 4S is a lot better in that regard and I happily leave "Location Services" switched on all the time. But I'd be reluctant to record a route (not that I have any great desire to) because that really does drain the battery.
Usually no, but it's a bit more complicated than that.
One answer would be to use a resistive touch screen, but they are generally considered not as good as capacitive, so you might need a cheap and nasty device to get one. (And maybe put up with having to use a stylus sometimes.)
I used Memory-Map on a Windows PocketPC PDA, which worked through a waterproof case, more or less, but that's died. I now have the maps on an Android phone which really doesn't work if my waterproof case is seriously wet.
At least one case claims to allow full use of your phone when underwater:
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there are a few waterproof Sonys which claim "wet finger tracking"
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'The Xperia Acro maintains the same level of responsiveness and accuracy when the screen is wet, or held under water, as it does in its normal dry state thanks to its unique "wet finger tracking".'
might not actually say "At the next rock, turn left", but you can pre-plan your route, and follow it with a crumb trail on the map, and it bleeps when you get to each waypoint.
Often thought there ought to be something with the form factor of a waterproof Kindle with E-ink display that operates as "press this button and re-centre the map on your current position" rather than continuously updating an LCD display - a bit like the size of a folded OS map without always being on a fold or corner.
It would consume little or no power most of the time, and be easily readable in sunlight. Walkers don't need rapid map updates - and a live breadcrumb trail could be added without rewriting the whole display.
And colour e-ink is supposed to be on the way, even if the colour is a bit washed out and limited compared with LCD screens it should be useful for displaying maps:
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