Maybe, says the Tenth Circuit in a rare victory for a prisoner under the Religious Land Use and Institutionalized Persons Act of 2000 (Yellowbear v. Lampert (10th Cir. Jan. 23, 2014)). On the facts of this case, the court says, the prison hasn’t shown that it has a compelling reason for denying such sweat lodge access to a particular prisoner. (Note that this particular prison already has a sweat lodge.) The prisoner’s RLUIPA case can thus go to trial before the district court, for a determination on whether there is indeed such a compelling reason in this situation.
The opinion is long, but quite readable, even by laypeople; if you’re interested in prisoner religious rights questions, check it out.