This article reports a cryogenic study on wideband shear horizontal surface acoustic wave (SH-SAW) devices based on an emerging Y-cut LiNbO3/SiO2/ sapphire lithium niobate on sapphire (LNOS) platform. To perform a comprehensive study, low-loss acoustic delay lines (ADLs) equipped with unidirectional transducers were designed with a wavelength (lambda) of 4 mu m(900MHz ) and a wide fractional bandwidth (FBW) of around 7% , featuring various physical delays ranging from 5 lambda to 200 lambda as testing structures. By cooling the temperature down to 5 K, the insertion loss (IL) of the longest ADL and the extracted propagation loss (PL) were characterized as 4.1 dB/mm and 3.5 dB/mm , respectively. Compared with an IL of 5.78 dB and a PL of 4.37 dB/mm at 275 K, the temperature-dependent acoustic losses diminish at low temperatures, with the overall PL dominated by the acoustic waveguide formed by the acoustic velocity mismatch between layers. Furthermore, a one-port resonator (lambda=2.8 mu m) with a large perceived effective electromechanical coupling greater than 40% was also characterized using the same technique, showing a 2x boost in the maximum Bode- Q at cryogenic temperatures. This study not only characterized the acoustic properties of wideband LNOS SH-SAW devices but also validated their excellent performance across a wide temperature range, suggesting their potential applications in cryogenic phononic circuits.