Observations by the DIRBE instrument aboard the COBE spacecraft, collected in 10 wavelength bands spanning the near-infrared to the far-infrared in a 0 degrees 7 beam, are presented for a region covering much of the Orion constellation. For an adopted distance of 450 pc, the total luminosity from dust (from 12 to 240 mu m) throughout the Orion A, Orion B, and lambda Ori fields, covering 16,900 pc(2), is similar to 10(6) Lo.. About 24%-36% of this dust luminosity is the result of dust heating by a general interstellar radiation field, with the rest resulting from heating by the Orion OB1 and lambda Ori OB associations. Given that the luminosity of the Orion OB1 and lambda Ori OB associations is 2.5 x 10(6) L., and also given that up to similar to 76% of dust luminosity is caused by dust heated primarily by the Orion stars, less than or similar to 30% of the stellar luminosity is trapped within the clouds and intercloud medium of Orion and reradiated at mid- to far-IR wavelengths. The near-IR (1.25, 2.2, 3.5, and 4.9 mu m) spectral distributions of the Orion Nebula and NGC 2024 indicate the presence of hot (T similar to few x 10(2) K) dust, both because of large I-V(4.9 mu m)/I-V(1.25 mu m) ratios and because of a substantial excess in the 3.5 mu m band relative to the intensities in the adjacent bands, some of which (greater than or similar to 30%) is caused by the 3.28 mu m emission line, commonly attributed to polycyclic aromatic hydrocarbons (PAHs). In the far-IR, the 100, 140, and 240 mu m intensities are consistent with a cool (usually 18-20 K, for emissivity index = 2) single-temperature component. The I-V(60 mu m)/I-V(100 mu m) color temperature is similar to 5-6 K higher than that from the cool component, suggesting that an additional warmer component or stochastically heated dust is contributing appreciably to the 60 mu m emission. Consequently, dust column densities derived from the 60 and 100 mu m intensities, assuming grains in thermal equilibrium, underestimate the dust-to-gas ratio by factors of 5-10. In contrast, the 140 and 240 mu m intensities yield dust column densities consistent with reasonable dust-to-gas mass ratios (i.e, similar to 0.01) to within a factor of 2. However, within this factor of 2, there appears to be a temperature-dependent systematic error in the dust column density derivation. The results of this paper may apply to external galaxies, since the region studied is more than 200 pc in size. All the above conclusions would have been obtained if the stars and clouds of Orion were placed at the distance of a nearby galaxy (similar to 1 Mpc) and observed in the DIRBE wavelength bands in an similar to 1' beam (provided the signal-to-noise ratio was unaffected). Hence, observations of the interstellar medium (ISM) in external galaxies that have resolutions of similar to 100 pc can still yield meaningful results. Further, if the stars and clouds in a spiral galaxy's arms can be represented by a series of Orion star and cloud complexes, one would expect the surface luminosity in the arms (for lambda=12-240 mu m) to be 2-4 times that in the interarm regions, averaged over 100 pc scales.