Big Bend NP is open - with the exception of all visitor centers.
Subject to change anytime, of course.
However, before you decide to go, do take note and read the second alert on this page.
https://www.nps.gov/bibe/index.htm
It reminds everyone that if you don't already have camping reservations, you will likely be disappointed. February, March and April are the high season and all camping, backcountry sites and lodge rooms are booked long in advance.
There are a couple of "campgrounds" outside the Park in Terlingua/Study Butte or Stillwell, but they are rather - saying this politely - spartan. (
b often not capitalized : marked by simplicity, frugality, or avoidance of luxury and comfort. ) And supplies are difficult to obtain in the best of circumstances so don't count on making any specific purchases. Do your homework before taking that 300+ mile drive from anywhere.
--
Alan