While I'd like to see different-headed weapons/tools in the game, I think it's important for the clarity of the game experience, to make one "bit" (or side of the head) be primary, and while the other might offer additional combat options, I don't think it should offer additional tool options.
I think it should. If we can tolerate battle axes used for woodcutting(halberds and all axe weapons allow coodcutting actually), then an axe/pick wouldn't be unfeasible.
I however am hoping for a revamped tool/weapon system sometime soon.
A dwarf should be able to carry an axe, a pick and a dagger/knife around. The current weapon combination limitations are due to an underdeveloped inventory system and the 'single weapon' dwarf designation.
The profession-limitations(no miner/woodcutters) are in turn based on the inability of both of the above. If both M/W could be activated, dwarves would pick up and drop axes and picks nonstop in a loop, like how they chase over to pickup two-handed weapons but don't. Two-handed weapons are removed from fortress mode and the dwarf files for a reason(it can be overridden if you allow '2' weapons).
My current dwarves are all miners unless they are important. If they are legendary miners, they become woodcutters(and only mine important stuff, taking up mining when i got lots of ore and gems ready and i draft the other bunch). Every dwarf left is armed with an axe(they're all hunters ... in plate).
This stuff is what needs fixing. Every dwarf armed to the teeth, running around with kickass combat skills. Fearless of combat when needed! The miners when somewhat skilled and in plate can be recruited on the fly and pack a punch! And altogether content with running around in heavy combat armor all days of the week!
Dwarves should be able to all wear armor. Tolkien's dwarves wore mail as we wear t-shirts. I also think they should all be able to carry all the tools for all of the professions! Given enough packs, pouches, slings, quivers, straps, sheathes etc.
However, they shouldn't WANT to! They should get discomfortable and sweaty and cranky and outright dump stuff they dont think they need. Say a miner would drop his axe, keeping the pick, keeping only his metal cap of the armor to protect the noggin. And maybe a single layer of mail.
Not every dwarf should have the mentality of a fighter and go roaring off into combat at the whim of the overlord! Most of them should be wusses who curl up and beg for their lives rather than risk to anger attackers by defending themselves! I mean, the goblins should be more likely to let them live, than the elves are. Goblins should be plenty willing!
We'd need more than a speed decreace which they'll be mostly blind for. They should WANT an axe-pick to lighten the load of both an axe and a pick!
Better yet, why not introduce additional tools? Say that a log has to be de-barked with an adze before normal use? It'd be like butchering an animal. Woodcutters would need axe-adzes more than anything else.