Guadalupe Mountains National Park is off the beaten path. I would worry about the weather more than crowds. There could be freezing rain and snow, so pack accordingly.
Few years ago, we drove out to the Davis Mountains during Spring break. We did not encounter crowds. There are miles and miles of Texas ... enough for everyone.
Check out
AmericanSouthwest website. Lots of good information by someone who has been there.
Take your camera and bring back some awesome pictures.
Later:
I decided to write a blogpost on Guadalupe Mountains National Park. Lots of good links for you. I am jealous now.