What zone are you in?

Location?

Watertown? Long Island? Big difference in plant material.

Would you say it's 'marshy'? Wet year-round?

Are you looking for evergreen or deciduous? How tall?

The deer would be harder to deal with than finding moisture thriving shady plants. If deer gather, your spot is wired into their brains

Here's a site to moist shade plants to give you an idea of what's out there. I have nothing to do with the site beyond finding it on Google.

Here is a link that might be useful: Deer resistance is another story

In zone 7a I rely on the following shade tolerant plants that deer avoid:

Pieris japonica
Skimmia japonica
Ferns (any species)
Rhododendrons

Actually, most of what I grow has to be deer resistant, and there are lots of trees and shrubs that are options. I had a bigger problem with shade loving options and deer. How deep is that shade? Is it shaded all day? Ornamental grasses need sun. The clumping bamboo in the picture are deer proof but they do get some sun.

nandina, mahonia, sarcoccoca hellebores. and they do not touch my hollies...but they will most likely not have berries.

Mahonia, that is one shrub I have been meaning to add! Shadyplace, I was going to put holly on my short list but have read that some people have said that their holly is eaten by deer. Guess it depends on the severity of the Winter. I did notice deer eating some of my Japanese Holly this past winter, but I agree that Holly is NOT a deer favorite. But as you suggest, to thrive, holly does need some sun and don't think of it as a understory shade shrub/tree.
P.S., Japanese Holly survived quite despite the experimental munching by local deer.

Also check out buttonbush for deer resistance.