There is a conflict, though. A tool is not considered a weapon, and will conflict with an existing uniform. So if you try to assign your wood-cutter a uniform to wear over his clothes/when he is off duty, he'll be unable to actually cut wood. If he has an axe already (and one assigned for his uniform), he'll actually drop it and go find another axe to use when you call him to duty.
However, if a dorf has high levels of mining skill and you tell him to pick any weapon to use, he'll often grab a pick.
About hunters, you can't just have ammo lying around and expect them to utilize the first thing they grab. There are actually three different ammo designations (war, training, hunting) found buried (somewhere) in the military screen. You have to go through and enable each specific stack for each specific duty. This is why hunting migrants always stop working- once they empty their original quiver, if you haven't specifically assigned them more ammo they'll have nothing to do. Bone bolts have annoyingly small stack sizes (5), and are fairly weak... but they are good enough to hunt with typically. Just don't send a single novice hunter armed with 5 bone bolts against a herd of elephants.. scratch that. Just never let a hunter go after elephants. >.> If you want to kill those you need to send a military squad out "hunting" or use traps.