The HI 21-cm optical depth ( ) can be considerably large as the kinetic and spin temperature of the inter-galactic medium(IGM) is expected to be very low during cosmic dawn. It will be particularly higher at regions with HI over-density. We revisit the validity of the widely used linearized equation for estimating the HI 21-cm differential brightness temperature ( ) which assumes << 1 and approximates [1 − exp(− )] as . We consider two scenarios, one without any additional cooling mechanism or radio background ( referred as standard scenario) and the other (referred as excess-cooling scenario) assumes the EDGES like absorption profile and an excess cooling mechanism. We find that given a measured global absorption signal, consistent with the standard(excess-cooling) scenario, the linearized equation overestimates the spin temperature by ∼ 5%(10%). Further, using numerical simulations, we study impact that the large optical depth has on various signal statistics. We observe that the variance, skewness and kurtosis, calculated at simulation resolution (∼ 0.5ℎ −1 Mpc), are over-predicted up to ∼ 30%, 30% and 15% respectively for the standard and up to ∼ 90%, 50% and 50% respectively for the excess-cooling scenario. Moreover, we find that the probability distribution function of is squeezed and becomes more Gaussian in shape if no approximation is made. The spherically averaged HI power spectrum is over predicted by up to ∼ 25% and 80% at all scales for the standard and excess-cooling scenarios respectively.