First up-close images of Mars’s little-known moon Deimos

> "a gravitational field of about 0.15 g is necessary to provide effective orientation information"

That's slightly less than lunar gravity (0.165 g). But, it's about the minimum amount needed to be able to use gravity to detect orientation, and is not necessarily enough to detect it reliably. That's thought to be one reason astronauts fell so often on the moon, although there were certainly other factors as well.

The paper also observes:

> Benson [30] showed that 0.22 g was not adequate to provide a vertical reference during experiments in the International Microgravity Laboratory (IML-1) on board Spacelab and Clément et al. [31] showed that in microgravity, 0.5 g provided by a centrifuge was enough to produce a perceived tilt of 90°. These values suggest that indeed it is likely to be the case that even after adaptation to a microgravity environment, forces in excess of 0.15–0.3 g are required to provide a behaviourally useful gravitational reference.

To answer your question, since vision is an important part of our orientation mechanism (also analyzed in the linked paper), it's likely that astronauts on the moon would have more difficulty with their eyes closed. Not necessarily that they'd have no sense of up at all, but that it wouldn't necessarily be accurate, so if they tried to walk with their eyes closed, they'd be much more likely to fall.

Alan Shephard and Ed Mitchell reported that the 7 degree tilt of their lunar module interfered with their sleep, which suggests it was noticeable. But it would be hard to point to something in their cabin arrangements that didn't interfere with sleep.