According to NM State Parks, only the following parks are open:
Cimarron Canyon State Park
Ute Lake State Park
Brantley Lake State Park
Sumner Lake State Park
Caballo Lake State Park
Cerrillos Hills State Park
Storrie Lake State Park
Villanueva State Park
Apparently part of their criteria for reopening a park is their ability to control the number of people at the park, and they say Elephant Butte is closed because of it's potential for large gatherings.
From
NM State Parks:
Elephant Butte Lake State Park (Park) remains closed due to the potential for large gatherings in the Park as the order prohibiting mass gatherings remains in effect to reduce the transmission of the COVID-19 virus. Accessing the Park from State Parks managed property is prohibited during this closure, and access to the lake surface within park boundaries is also prohibited.
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I doubt very seriously it'll be open.