One major challenge in cryoseismology is that signals of interest are often buried within the high noise level emitted by a multitude of environmental processes. Events of interest potentially stay unnoticed and remain unanalyzed, particularly because conventional sensors cannot monitor an entire glacier. However, with Distributed Acoustic Sensing (DAS), we can observe seismicity over multiple kilometers. DAS systems turn common fiber-optic cables into seismic arrays that measure strain rate data, enabling researchers to acquire seismic data in hard-to-access areas with high spatial and temporal resolution. We deployed a DAS system on Rhonegletscher, Switzerland, using a 9 km long fiber-optic cable that covered the entire glacier, from its accumulation to its ablation zone, recording seismicity for one month. The highly active and dynamic cryospheric environment, in combination with poor coupling, resulted in DAS data characterized by a low Signal-to-Noise Ratio (SNR) compared to classical point sensors. Our objective is to effectively denoise this dataset. We use a self-supervised J-invariant U-net autoencoder capable of separating incoherent environmental noise from temporally and spatially coherent signals of interest (e.g., stick-slip or crevasse signals). The method shows enhanced inter-channel coherence, increased SNR, and significantly improved visibility of the icequakes. Further, we compare different training data types varying in recording position, wavefield component, and waveform diversity. Our approach has the potential to enhance the detection capabilities of events of interest in cryoseismological DAS data, hence to improve the understanding of processes within Alpine glaciers.