We report unusual near- and mid-infrared photometric properties of G 196-3 B, the young substellar companion at 16'' from the active M2.5-type star G 196-3 A, using data taken with the IRAC and MIPS instruments onboard Spitzer. G 196-3 B shows markedly redder colors at all wavelengths from 1.6 up to 24 μm than expected for its spectral type, which is determined at L3 from optical and near-infrared spectra. We discuss various physical scenarios to account for its reddish nature and conclude that a low-gravity atmosphere with enshrouded upper atmospheric layers and/or a warm dusty disk/envelope provides the most likely explanations, the two of them consistent with an age in the interval 20-300 Myr. We also present new and accurate separate proper motion measurements for G 196-3 A and B confirming that both objects are gravitationally linked and share the same motion within a few mas yr-1. After integration of the combined spectrophotometric spectral energy distributions, we obtain the result that the difference in the bolometric magnitudes of G 196-3 A and B is 6.15 ± 0.10 mag. Kinematic consideration of the Galactic space motions of the system for distances in the interval 15-30 pc suggests that the pair is a likely member of the Local Association and that it lies near the past positions of young star clusters like α Persei less than 85 Myr ago, where the binary might have originated. At these young ages, the mass of G 196-3 B would be in the range 12-25 M Jup, close to the frontier between planets and brown dwarfs.