[Keith Rogan]

I've seen a lot of stuff over the years about moon phases and the effect on game, and in my opinion most of it is silly.
I think, as you say, that a bright moon allows animals to feed more at night and so you see less of them during the day.
But there's a lot other variables revolving around weather, etc, that affect them as well, and most of that can be summed up in the thought "where would I be most comfortable?" Deer are not immune to weather and they'll look for bedding places based on that.
Most of my experience over the last dozen years is around Sitka Blacktails, but I'm sure this would apply to any game animal.
If it's a hot day early in the season, look for deer on the shady sides of hills where they can catch a breeze to blow away bugs.
If it's a cold day late in the season, look for them in a sunny side of the hills on the slope away from the wind.
If it's raining, look in the dark timber - snow, same deal because they don't want to break through deep snow any more than you do.

To summarize this, I'd say to just think of animals as having the same needs as humans. Just think in terms of laying up for the whole day and where you'd be most comfortable and safe if you did that... Take into account weather, bugs, hunting pressure and last but not least - visibility. Meaning you'll find them back on that shelf that you just can't see into rather than on the exposed hillside.

All of this is going to be different in your area - maybe it's dry and you need to take water into account, or flat so the hillside thing doesn't apply. No matter, just think about where you'd like to be and that's where the deer will be.