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Yes, it is legal but let me explain.
The employer can't deduct your paycheck if you don't work those additional hours. That would be an illegal deduction from pay, as your employer's office is shut and you (presumably) are available for work but can't because they aren't open.
However, as a salaried exempt employee, the employer can legally request you to work any number of hours and even track those hours, not for purposes of deducting pay, but for purposes of determining if you are following instructions on required work production. If you don't meet that requirement, while your check can't be reduced, you can be otherwise punished for not obeying. The employer could deduct from your vacation, cut your pay (meaning permanently), suspend you from work without pay, demote you or even terminate you.
I know this seems a very narrow distinction, but the FLSA is clear that it only intended to effect your paycheck and that's it. If the employer doesn't illegal deduct time from your ultimate pay, then it's legal to do any of these other things I have mentioned.