Autonomic sleep staging refers to sleep characterization using autonomic physiological signals. This paper focuses on utilizing electrodermal activity (EDA), an autonomic signal that reflects the activity of sympathetic nerves on sweat glands, for characterizing wake and three sleep stages viz., light, deep, and rapid eye movement (REM) sleep. The study also investigates whether skin temperature (ST) measured from the same skin site as EDA can enhance the performance of EDA-based sleep staging. EDA and ST during sleep were recorded overnight to generate 118 datasets with an average duration of 6.2 h. Recordings were done from the dominant ventral wrist of all subjects using a GEN II wrist wearable vital signs monitor (VSM) from Analog Devices. WatchPAT, an FDA-approved, portable sleep monitor was used as a reference to generate the ground truth. 204 features were extracted from 30-s epochs of raw and preprocessed EDA and ST signals. Feature selection using a novel ensemble wrapper method was adopted to identify the best feature subset. User-specific, general, and non-intersecting ordinal models based on 7 classifiers were investigated, concerning their utility for sleep staging. While the EDA-based scheme using the non-intersecting ordinal random forest classifier yielded the highest training accuracy of 88.11% for females and 88.75% for males, the addition of ST enhanced it to 96.29% and 95.06%, respectively. The scheme exhibited good generalizability on a new dataset, yielding an accuracy of 94.11% for females and 92.92% for males. The duration of wake, light, deep, and REM was estimated as a percentage of total sleep duration and was validated against the reference. The sleep estimates showed a positive correlation with Pearson’s r of 0.97, 0.96, 0.96, and 0.98 respectively for %Wake, %Light, %Deep, and %REM. The Bland–Altman analysis done on estimates also indicated similarity with minimal bias.