I bought a small 75 lb anvil a while back at an auction sale and it was rusted from head to toe. I recently just got around to restoring it and decided to soak it in an apple cider vinegar bath for about a week to help take the rust off. I gave it a good rinse off after I took it out and it started leaking black from the hardy hole to the horn of the anvil. This thing is pretty beat up but the fact that it leaked black really surprised me. Anyone got any idea what it could be?

Not sure what you mean by "leak"...sweated?  Remember that iron is porous so it might be losing some stuff that soaked into the various pores.  Top plate not so much as the cast but even good steel is slightly porous in a chemical sense.

Probably ferrous oxide rather than ferric oxide (rust)   "Iron(II) oxide or ferrous oxide is the inorganic compound with the formula FeO. Its mineral form is known as wüstite. One of several iron oxides, it is a black-colored powder that is sometimes confused with rust, which consists of hydrated iron(III) oxide (ferric oxide)."  (wiki attribution)

Sometimes corroded iron that has been oxygen deficient will "bleed" black rather than reddish rust due to the ferrous oxides.  Most people see this inside pipe threads when disassembled but it can happen in the various micro-pores of the material too.

It wouldn't surprise me to see any vinegar solution weaken and break down whatever gunk has accumulated in the hardy hole, causing it to run.  

You've got a good looking anvil and you should be happy with it.  As long as it has a solid rebound, you're good.

ferrous acetate  I'd be suspicious of a possible crack or delamination of the face if it's leaking out after a through rinse.