Long answer: Yes, for a few seconds quite frequently, because I feel that it allows me to get a better feel for the music, the harmony, the metrics, check if all players are "in tune". It all flows - I open my eyes lookt at the band and we all have and sense that inner smile that is so satisfying. Your open eyes can distract you from all that.
Since I was a kid, I always liked to close my eyes and walk. It's both exhilarating and a bit scary because you might get hurt.
There are two versions of the game, 1) open your eyes only randomly and at long intervals. Try to judge the distances and keep in mind a mental picture of what you're about to walk though and 2) It's also really fun to find a really big field, close your eyes and just walk out into it with abandon. At some point I like to open them and see where in the field I ended up and if I kept going straight ahead or not.