  We present a detailed analysis of the impact of $H_0$ priors from recent
surveys in the literature on the late time cosmology of five $f(T)$
cosmological models using cosmic chronometers, the Pantheon data set, and
baryonic acoustic oscillation data. In this work, we use three recently
reported values of $H_0$ that have contributed to the recent $H_0$ tension
problem. We find that these priors have a strong response in these analyses in
terms of all the cosmological parameters. In general, our analyses gives much
higher values of $H_0$ when considered against equivalent analyses without
priors while, by and large, giving lower values of the matter density
parameter. We close with a cross-analysis of each of our model, data set and
prior combination choices.
