Context. We study the stellar population of the very young cluster NGC 2362, using a deep Chandra ACIS-I X-ray observation. This cluster, only 5 Myr old, has already cleared most of its inter- and circumstellar dust, and with its small and uniform reddening offers a unique opportunity of studying its pre-main-sequence stellar population with minimal disturbance from a dense interstellar medium. Aims. Our main purposes are to select cluster members down to low masses and to study their properties as a population (spatial properties, initial mass function, and coronal properties). Methods. We compare existing deep optical photometry and H α data with new X-ray data. We use combined optical and X-ray criteria to select cluster members. Results. We detect 387 X-ray sources down to $\log L_{\rm X} = 29.0$ (erg/s), and identify most of them (308) with star-like objects. The majority (88%) of optically identified X-ray sources are found to be very good candidate low-mass pre-main-sequence stars, with minimal field-object contamination. This increases the known cluster census by a substantial amount at low masses, with respect to previous optical/IR studies. The fraction of stars with active accretion is found to be in the range 5–9%. We find a significantly wider spatial distribution for low-mass stars than for massive stars (mass segregation). We find only a small spread around the low-mass cluster sequence in the HR diagram, indicating that star formation lasted only about 1–2 Myr. We have derived the cluster initial mass function, which appears to flatten (on the low-mass side) at higher masses with respect to other very young clusters. The quiescent X-ray emission of low-mass cluster stars is found to be rather strictly correlated with the stellar bolometric luminosity: the small spread in this correlation puts an upper bound on the amplitude of X-ray variability on time scales longer than one day (e.g., activity cycles) in such young coronal sources. We find significant X-ray spectral differences between low-mass stars brighter and fainter than $\log L_{\rm X} \sim 30.3$ (erg/s), respectively, with X-ray brighter stars showing hotter components ($kT \sim 2$ keV), absent in fainter stars.