I'm curious in your Wing Chun studies, do you guys ever apply Buddhist, Daoist, or other eastern philosophies in your training?

Somewhat. This concept of a "center line" is a huge aspect of Ving Tsun. When you start, it's just an imaginary vertical line down the center of your body, and your priority is to control it. But the more you learn and study, the more it takes on a much broader idea of balance. You can't be too hard, or too relaxed. You can't train one thing to the exclusion of all others. You can't train to the exclusion of life. When I expressed some frustration to my sifu (teacher) about how dull my job can be, he mentioned the possibility of too much yang. Not in the sense of some weird metaphorical energy, just the idea that I was pushing life too hard, and that sometimes you need to just be still and go with it, even if you don't want to.

But it's something we don't generally talk about until you've been there a lot longer.

I wouldn't say it's overt, though. My teacher isn't a Daoist, but his advice on things usually ends up having that flavor, such as the example above. By way of another example, our emphasis on physical relaxation means this verse from the Dao De Jing (chapter 43) applies as much to our physical actions as anything more metaphorical:

The softest things of the world

Override the hardest things of the world

That which has no substance

Enters into that which has no openings

I've certainly seen that in my training; a relaxed hand will fit into spaces that it seems far too big for.

But honestly it's tough to explain without context, i.e. the listener having some experience with the art. My impression is that these eastern religions don't really separate things into distinct spheres the way we tend to in the West.

*My family spells it Ving Tsun (rather than Wing Chun) because of some internecine politics that I'm only dimly familiar with.

Westerns, etc.

Perhaps. I've seen some samurai movies that I like, but westerns usually don't do it for me. My enjoyment of kung fu movies is almost exclusively the spectacle of combat, not really the story (or what passes for one) that holds it all together.