I would think it would be preferrable to close your eyes when meditating, simply becuase you will be more rested that way, so you can focus on your meditating without having to blink, or your eyes getting tired :)
Even when I close my eyes they sometimes open slightly but I don't notice it until I'm finished meditating and I realize my eyes were opened slightly the whole time. But if you prefer it having your eyes open then relax your eyelids and let them "fall" to place whether that closed, opened or half closed etc. if your eyes happen to be open you can always darken the place somehow where your meditating so you won't get distracted by your surrounding. Just a suggestion
I am to tired to read other peoples replies to your post, no offense to anyone. However the most important thing about visualizing is being comfortable and doing it your own way, so if you've been doing it a certain way, keep doing that. If you ask others for their advice or instructions on ways to visualize that may disrupt your natural ability. Visualizing is all about seeing, using your heart and mind to paint a picture for you, so keep your eyes open. That's the bext advise I can give at the moment.