Sherry,
I didn't make it to the gate last week because the road was still snowed over a few miles below, but based on your description of the road I would recommend using your knobby tires pumped up to the maximum pressure they will safely tolerate (molded on the sidewall of your tire, probably around 50 psi on a 24 inch knobby tire). In the rocks the biggest danger will be pinch flats where the tire/tube get folded between the rim and a rock and get a double-cut that looks like a snakebite. Unfortunately pinch flats can't usually be patched, so bring extra tubes and a pump and practice changing them before you go. You might also try running pre-slime-filled tubes available at Walmart, although they are better at sealing little holes from thorns than pinch-flats. If you find yourself spinning the rear tire on loose soil you can let a little air out to gain traction, but you'll increase your risk of flatting.
Good luck, I hope to get up there on my bike sometime later this summer...