When it comes to visualization it's not the physical eyes that you are going to "see" with, it's the mind's eye. If I now say the word "Batman" you think of that with images because that is the language that your brain is using, images and association. So in the same way that you use the mind's eye to see the image with eyes open, you can also see it with closed eyes. It's all about shifting what you focus on. It's difficult to describe exactly how this works because in short, we don't know.
I think you can get the feeling of what I am trying to describe.
So you should not think about what you do with your eyes, it doesn't really matter, the importance lies in the focus of your awareness!
A proof for that (that you can try yourself) is that I can move my eyes around in random movements and and circles but still hold a visualization image in my mind, no matter if the eyes are opened or closed.
We can all do this simple visualization by holding a mental image on our mind for a millisecond, but when it comes to actually keep that focus most of us struggle. And the reason for that is that we are unfocused. We are raised with shifting our focus all the time, from facebook notifications to textmessages etc. If you want to be able to maintain focus longer, you simply need to practise it.
A way to demonstrate that you already possess the ability to visualize, but the problem is maintaining focus, is to tell you to think about what you have done today, or to think of a memory. You are not only going to use words to describe that in your mind, you are going to use images! And by that time you are visualizing. But.. if you can't hold the images in your mind it's because you jump to another thought or image and that is why the image you tried to focus on falls apart.
You can either practise your focus directly with visualization by keeping your focus for as long as possible on an image, or you can practise meditation.
I have a guide on how to do that in my signature. 
When you can easily keep a still image or a simple object in your mind's eye both while having your eyes opened and closed, then you can start using other senses and move your focus in this internally created world.
But remember to both practise your visualization skills but also your ability to focus, because if you can't focus, your visualization aren't going to be stable enough to play around with anyway. And not your dreams either for that matter.
I hope this helps and if you have more questions, ask away. 
Peace!
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