So I grabbed myself a pickaxe because I wanted to mine. After a ten or fifteen I kind of got tired of seeing the animation. I decided to try something by tossing the pickaxe over to Lydia and see if I could deliver her a command to mine the ore. Oh wow! It really shows up under the reticle and I think she's about to mine it! She walks over to the node and gives me something along the lines of "nope, not doing that".

It never made much sense for my weak mage to be mining ore but since I received the transmutation spell recently, I wanted to make some gold jewelery. I think it'd be neat if Bethesda patched it so you could give followers these type of commands because all they're about one action away from doing it already!