I'm pretty sure the dwarves did use missile weapons. How else would they defend the Bridge of Khazad-dum, which seems to be built exactly to be defended with arrows.
Of course, there would be axe-wielding dwarves on the western end, but archers were certainly needed to pepper the attackers and not to allow them to form their own bowmen line on the eastern side of the bridge.
Besides, Thorin was pretty accurate with a bow, killing that deer over the Enchanted Stream, and firing an arrow directly to the messenger's shield. He didn't mean to kill him, I'm sure. Why the other dwarves weren't succesful shooting the animals in Mirkwood, I cannot say. Perhaps something was afoul with the squirrels there.