Assuming nothing else about the animal companion, if the animal companion wears a frost amulet of mighty fists, then the companion is the subject of a greater magic fang spell so that its natural weapon gains a +3 enhancement bonus, the animal companion benefits fully from both the amulet and spell.
(Unlike a typical magic weapon—see here—the amulet specifically says that it does not first need to grant a +1 enhancement bonus before it can grant magic weapon special abilities, so a frost amulet of mighty fists that grants no enhancement bonus is a legit standalone item.)
The magic weapon special ability frost from the amulet is priced as a +1 enhancement bonus and that +1 enhancement bonus counts toward the +10 maximum virtual enhancement bonus that a weapon can possess ("A single weapon cannot have a[n]… enhancement bonus plus [magic weapon] special ability bonus equivalents… higher than +10"; see here). However, the magic weapon in question—the animal companion's natural weapon—doesn't have an actual numeric enhancement bonus until the greater magic fang spell, so the greater magic fang spell functions normally and completely, granting its full bonus to the natural weapon.
Were this instead a +1 frost amulet of mighty fists, the greater magic fang spell's numeric enhancement bonus would overlap with the amulet's numeric enhancement bonus, and only the bigger enhancement bonus would apply, hence still just the +3. Further, the amulet's frost weapon special ability would continue to function normally in this case, too.