With the recent recommendations from the president, will the park be open this week?

Yes I just left this morning and they had no plans to close, as per the nice lady who I checked in with the Park isn't closing yet and they have been super packed all spring break

The last I read Texas state parks will be open but they recommend going to the we site and register, so you can print out the passes. You need to do this at least 2 days before your visit https://texasstateparks.reserveamerica.com/