The Art Newspaper surveyed museums in the US and came away with this information:

A survey of more than 60 major art museums in the US shows that the directors of more than one third have recently taken pay cuts, many of them substantial, and senior staff at most of those institutions have also had their compensation trimmed. The cuts range from salary reductions and forfeiture of bonuses to unpaid leave. Even where there have not been massive layoffs, hiring freezes leave posts vacant and incentives induce early retirement.

The report has a detailed list of institutions and the modifications made by senior staff.

Salary Cuts for One Third of US Museum Directors (The Art Newspaper)