The dominant low-frequency patterns of outgoing longwave radiation over the tropical Indian and western Pacific oceans in response to El Niño-Southern Oscillation (ENSO) during the northern winter are investigated using the nonlinear classification method of the self-organizing map (SOM), additionally aided by an empirical orthogonal function (EOF) analysis. There are at least two different air-sea coupled phenomena in the tropical Indian Ocean, i.e., the Indian Ocean Dipole (IOD) mode in late summer and fall and the Wind-Evaporation-Sea surface temperature (WES) feedback-driven mode in the winter and spring. The SOM results exhibit that the phase of WES becomes positive (negative) at the El Niño (La Niña) phase, which indicates a linear linkage of WES with ENSO. In contrast, few combined patterns of the negative IOD and the La Niña event can be extracted although the reversed pattern is prominent, suggesting a nonlinear-like relationship between IOD and ENSO. Since the ENSO-induced convective forcing over the tropical Indian and western Pacific oceans has strong asymmetric features with respect to the ENSO phase, the remote response of the East Asian winter monsoon to ENSO becomes complicated. At the El Niño event, the monsoon circulation in the southern part of East Asia tends to be attenuated in late winter through the dominance of the western North Pacific anticyclone in the lower troposphere, but at the La Niña event, the monsoon circulation over Korea and Japan is enhanced in early winter through the downstream development of stationary Rossby wave packets along the South Asian waveguide.