The study of cosmic neutrinos with energy 𝐸𝜈 ≥ 1014𝑒𝑉 is one of the most important and challenging
tasks in multi-messenger astrophysics. Detectors must operate in well shielded laboratories.
An alternative is provided by the observation of Horizontal Air Showers (HAS, i.e. showers with
a zenith angle ≥ 75◦) induced by neutrinos. With this technique the background of showers induced
by cosmic rays is heavily reduced due to the large atmospheric depth and by the exponential
attenuation of the shower electromagnetic component. In this contribution we discuss the HAS detection
toward the bright GRB 221009A by the LHAASO-KM2A detector showing the expected
differences of neutrino-induced events with surviving showers produced by cosmic rays. We introduce
a preliminary selection to reject the background and report on a search for 𝜈𝑒-induced
HAS (𝜃 ≥ 75◦) in temporal coincidence with the prompt phase of GRB 221009A.