  Radial velocity searches for extrasolar planets have recently detected
several very low mass (7-20M_Earth) planets in close orbits with periods <10
days. We consider the prospects for detecting the analogs of these planets in
Galactic open clusters via transits. We outline the requirements for
constructing a transit survey that would allow one to probe such ``Hot Earths''
and ``Hot Neptunes.'' Specifically, we present a simple criterion for detection
that defines the minimum aperture required to detect planets of a given radius
in a cluster at a given distance. Adopting photometric precisions that have
been demonstrated in state-of-the-art variability surveys, we then predict the
number of planets one could potentially detect with ambitious transit surveys
toward several open clusters. Dedicated surveys lasting more than 20 nights
with Pan-STARRS toward the Hyades and Praesepe could detect a handful of Hot
Earths, if the majority of stars host such planets. Similar surveys with larger
aperture telescopes (e.g. CFHT, MMT), toward M67, M35, M50, and M37 could
detect Hot Neptunes, provided that their frequency is >1%. The majority of
planets will be detected around M dwarfs; detecting Hot Neptunes around such
primaries requires photometric precisions of ~1%, whereas Hot Earths require
\~0.1%. We discuss potential hurdles in detecting and confirming small planets
in ground-based surveys, including correlated noise, false positives, and
intrinsic stellar variability.
