  The 21 cm signal from cosmic hydrogen is one of the most propitious probes of
the early Universe. The detection of this signal would reveal key information
about the first stars, the nature of dark matter, and early structure
formation. We explore the impact of an emissive and reflective, or `hot',
horizon on the recovery of this signal for global 21 cm experiments. It is
demonstrated that using physically motivated foreground models to recover the
sky-averaged 21 cm signal one must accurately describe the horizon around the
radiometer. We show that not accounting for the horizon will lead to a signal
recovery with residuals an order of magnitude larger than the injected signal,
with a log Bayesian evidence of almost 1600 lower than when one does account
for the horizon. It is shown that signal recovery is sensitive to incorrect
values of soil temperature and reflection coefficient in describing the
horizon, with even a 10% error in reflectance causing twofold increases in the
RMSE of a given fit. We also show these parameters may be fitted using Bayesian
inference to mitigate for these issues without overfitting and
mischaracterising a non-detection. We further demonstrate that signal recovery
is sensitive to errors in measurements of the horizon projection onto the sky,
but fitting for soil temperature and reflection coefficients with priors that
extend beyond physical expectation can resolve these problems. We show that
using an expanded prior range can reliably recover the signal even when the
height of the horizon is mismeasured by up to 20%, decreasing the RMSE from the
model that does not perform this fitting by a factor of 9.
