The end of Moore’s Law aligned with data privacy concerns is forcing machine learning (ML) to shift from the cloud to the deep edge. In the next-generation ML systems, the inference and part of the training process will perform at the edge, while the cloud stays responsible for major updates. This new computing paradigm, called federated learning (FL), alleviates the cloud and network infrastructure while increasing data privacy. Recent advances empowered the inference pass of quantized artificial neural networks (ANNs) on Arm Cortex-M and RISC-V microcontroller units (MCUs). Nevertheless, the training remains confined to the cloud, imposing the transaction of high volumes of private data over a network and leading to unpredictable delays when ML applications attempt to adapt to adversarial environments. To fill this gap, we make the first attempt to evaluate the feasibility of ANN training in Arm Cortex-M MCUs. From the available optimization algorithms, stochastic gradient descent (SGD) has the best trade-off between accuracy, memory footprint, and latency. However, its original form and the variants available in the literature still do not fit the stringent requirements of Arm Cortex-M MCUs. We propose L-SGD, a lightweight implementation of SGD optimized for maximum speed and minimal memory footprint in this class of MCUs. We developed a floating-point version and another that operates over quantized weights. For a fully-connected ANN trained on the MNIST dataset, L-SGD (float-32) is 4.20× faster than the SGD while requiring only 2.80% of the memory with negligible accuracy loss. Results also show that quantized training is still unfeasible to train an ANN from the scratch but is a lightweight solution to perform minor model fixes and counteract the fairness problem in typical FL systems.