I've actually read a good article on this (Deep hierarchies vs composition in game coding), unfortunately I can't find it. At any rate, the guy there advocated composition over inheritance whenever in doubt. I'll try to give you the gist of it as applied to your situation.
I honestly think that composition is the way to go (and not inheritance) when it comes to game coding. Usually, the case is you have some basic thing on which you want to put various behaviors in various combinations, rather than make it have one behavior and ALL other behaviors derived from that. I.E. your GameObject base class might support translation and rotation as all game elements should be able to do that. Further more only SOME of your game objects also need collision detection, and more-over some of them might need to emit particles. Now obviously, collision detection ability doesn't automatically imply "ability to emmit particles as well" nor does the other way around make sense. So rather than having CollidingGameObject extends GameObject and then ParticleEmittingGameObject extends CollidingGameObject (in order to be able to also have game objects that support collisions and particle emissions), it's much better to make a base Component class, extend from it a CollisionDetectionComponent (which can work with a GameObejct instance) and a ParticleEmitting component, then have your base GameObject class support multiple components (via composition, like a list of components field), and adding and removing of components. Sure, at the beginning it will be more tedious to code, but once you have all your major components implemented and the component-applying mechanism in place for the GameObejct class, it will be a lot easier to modify/refactor things later, plus your code will be more performant. This is how Unity have coded their engine.
So in your case, I'd make two Texture components, one for static and one for animated one, and then add them as needed on the GameObject base class (i.e. some GameObjects will only have 1 Static texture component, some will have 1 Static and 1 animated, and then later on if your fancy strikes you to make a dual turret tank, you can just add 1 Static and 2 Animated and you're good to go).