Personally I think that all Dwarven workers should be able to walk across mountains whenever they want. I mean, the majority of their people live inside of these things, surely they have found ways to easily traverse them. .
Not sure that I agree with the logic that living underground makes someone able to walk over hills/mountains easily, but would like to see tunnels added.
Perhaps one way to do this would be to have a Khazad Engineer unit (perhaps a National unit...or perhaps an option open to all Great Engineers, and thus all civs?) to be able to cast a Build Tunnel "spell" that in a similar way to bombard would affect a selectable neighbouring tile.
Would need a spell delay - and I'm thinking on the lines of 8-12 turns (ie; will usually average around 10 turns, but can take a little longer/shorter to represent different rock types/issues*). When the "spell" is finished the Mountain tile would be replaced with a new Mountain Tunnel tile which allows movement onto that tile.
* hmmm...or perhaps, have a turn delay of 5 turns - but for each turn their would be a 20% risk that the tunneling has to be restarted ("We've hit a seam of Obsidian/Granite - we'll have to start again!")
It would mean that the tile wouldn't be limited to one direction of travel (ie; a unit entering the tile could then enter any passable terrain neighbouring it)
Perhaps, "Mountain Tunnel" tiles could then be defined as being able to build improvements on by standard workers- mushroom farms, mines (with a higher chance of revealing bronze/iron/mithril/gems than hills) or fortifications - though possibly with a risk of tunnel collapse for the latter two (kills units (except flying) on tile, and reverts back to mountain)...