Alex-
Enjoy your day at Burning Tree. We are in the process of researching the golf course more, as to the architectural pedigree, construction, etc, but it is a Colt/Alison. MacKenzie was a "junior partner" at the time, hence you won't find anything resembling his work.
Look for the lack of fairway bunkering and abundance of left to right holes.
The holes playing near the Beltway were changed due to the road construction--10 was originally a par 5, 11 played at a different angle to the green, and I believe 12 and 13 were shortened as well.
Most greens are pretty quick, so stay below the hole. Not too much undulation to speak of, a lot of hidden breaks, and most are on the small side, befitting a course that requires accuracy.
Be sure to look at the various items in the clubhouse, e.g. clubs from ex-Presidents, flags hanging in the locker room, etc, it is a very special place.
The members sit at long tables to eat, and the area has a large picture window that looks out at 1 tee and down 1 fairway.
I absolutely love the club logo.
As far as a public layout in the area...we've had some discussions about this in the past. My recommendation is for Beechtree or Bulle Rock, which are both about an hour north on 95, although if you head up 270 towards Frederick, there are a number of quality, high-end publics in that area as well.