  The Wide-Field Infrared Transient Explorer (WINTER) is a new 1 $\text{deg}^2$
seeing-limited time-domain survey instrument designed for dedicated
near-infrared follow-up of kilonovae from binary neutron star (BNS) and neutron
star-black hole mergers. WINTER will observe in the near-infrared Y, J, and
short-H bands (0.9-1.7 microns, to $\text{J}_{AB}=21$ magnitudes) on a
dedicated 1-meter telescope at Palomar Observatory. To date, most prompt
kilonova follow-up has been in optical wavelengths; however, near-infrared
emission fades more slowly and depends less on geometry and viewing angle than
optical emission. We present an end-to-end simulation of a follow-up campaign
during the fourth observing run (O4) of the LIGO, Virgo, and KAGRA
interferometers, including simulating 625 BNS mergers, their detection in
gravitational waves, low-latency and full parameter estimation skymaps, and a
suite of kilonova lightcurves from two different model grids. We predict up to
five new kilonovae independently discovered by WINTER during O4, given a
realistic BNS merger rate. Using a larger grid of kilonova parameters, we find
that kilonova emission is $\approx$2 times longer-lived and red kilonovae are
detected $\approx$1.5 times further in the infrared than in the optical. For
90% localization areas smaller than 150 (450) $\rm{deg}^{2}$, WINTER will be
sensitive to more than 10% of the kilonova model grid out to 350 (200) Mpc. We
develop a generalized toolkit to create an optimal BNS follow-up strategy with
any electromagnetic telescope and present WINTER's observing strategy with this
framework. This toolkit, all simulated gravitational-wave events, and skymaps
are made available for use by the community.
