We introduce a time-domain framework for efficient multichannel speech enhancement, emphasizing low latency and computational efficiency. This framework incorporates two compact deep neural networks (DNNs) surrounding a multichannel neural Wiener filter (NWF). The first DNN enhances the speech signal to estimate NWF coefficients, while the second DNN refines the output from the NWF. The NWF, while conceptually similar to the traditional frequency-domain Wiener filter, undergoes a training process optimized for low-latency speech enhancement, involving fine-tuning of both analysis and synthesis transforms. Our research results illustrate that the NWF output, having minimal nonlinear distortions, attains performance levels akin to those of the first DNN, deviating from conventional Wiener filter paradigms. Training all components jointly outperforms sequential training, despite its simplicity. Consequently, this framework achieves superior performance with fewer parameters and reduced computational demands, making it a compelling solution for resource-efficient multichannel speech enhancement.