Changes in snow cover over the Tibetan Plateau (TP) have a significant impact on agriculture, hydrology, and ecological environment of surrounding areas. This study investigates the spatio-temporal pattern of snow depth (SD) and snow cover days (SCD), as well as the impact of temperature and precipitation on snow cover over TP from 1979 to 2018 by using the ERA5 reanalysis dataset, and uses the Mann–Kendall test for significance. The results indicate that (1) the average annual SD and SCD in the southern and western edge areas of TP are relatively high, reaching 10 cm and 120 d or more, respectively. (2) In the past 40 years, SD (s = 0.04 cm decade−1, p = 0.81) and SCD (s = −2.3 d decade−1, p = 0.10) over TP did not change significantly. (3) The positive feedback effect of precipitation is the main factor affecting SD, while the negative feedback effect of temperature is the main factor affecting SCD. This study improves the understanding of snow cover change and is conducive to the further study of climate change on TP.