The combination of orthogonal frequency modulation (OFDM) and multiple-input multiple-output (MIMO) systems plays an important role in modern communication systems. In order to meet the growing throughput demands, future MIMO-OFDM receivers are expected to utilize a massive number of antennas, operate in dynamic environments, and explore high frequency bands, while satisfying strict constraints in terms of cost, power, and size. An emerging technology to realize massive MIMO receivers of reduced cost and power consumption is based on dynamic metasurface antennas (DMAs), which inherently implement controllable compression in acquisition. In this work we study the application of DMAs for MIMO-OFDM receivers operating with bit-constrained analog-to-digital converters (ADCs). We exploit previous results in task-based quantization to show how DMAs can be configured to improve recovery in the presence of constrained ADCs, and propose an algorithm for adjusting the DMA parameters based on channel state information. Our numerical results demonstrate that the DMA-based receiver is capable of accurately recovering OFDM signals, and that its performance is comparable to receivers operating without bit limitations, while being significantly less costly and more power efficient.