Monitoring the snow water equivalent (SWE) in the harsh environments of high mountain regions is a challenge. Here, we explore the use of muon counts to infer SWE. We deployed a muonic cosmic ray snow gauge (mu-CRSG) on a Swiss glacier during the snow-rich winter season 2020/21 (almost 2000 mm w.e.) The mu-CRSG measurements agree well with measurements by a neutronic cosmic ray snow gauge (n-CRSG), and they lie within the uncertainty of manual observations. We conclude that the mu-CRSG is a highly promising method to monitor SWE in remote high mountain environments with several advantages over the n-CRSG.