  We analyze line-of-sight atomic hydrogen (HI) line profiles of 31 nearby,
low-mass galaxies selected from the Very Large Array - ACS Nearby Galaxy Survey
Treasury (VLA-ANGST) and The HI Nearby Galaxy Survey (THINGS) to trace regions
containing cold (T $\lesssim$ 1400 K) HI from observations with a uniform
linear scale of 200 pc/beam. Our galaxy sample spans four orders of magnitude
in total HI mass and nine magnitudes in M_B. We fit single and multiple
component functions to each spectrum to isolate the cold, neutral medium given
by a low dispersion (<6 km/s) component of the spectrum. Most HI spectra are
adequately fit by a single Gaussian with a dispersion of 8-12 km/s. Cold HI is
found in 23 of 27 (~85%) galaxies after a reduction of the sample size due to
quality control cuts. The cold HI contributes ~20% of the total line-of-sight
flux when found with warm HI. Spectra best fit by a single Gaussian, but
dominated by cold HI emission (i.e., have velocity dispersions <6 km/s) are
found primarily beyond the optical radius of the host galaxy. The cold HI is
typically found in localized regions and is generally not coincident with the
very highest surface density peaks of the global HI distribution (which are
usually areas of recent star formation). We find a lower limit for the mass
fraction of cold-to-total HI gas of only a few percent in each galaxy.
