We report unusual near- and mid-infrared photometric properties of G 196-3 B, the young substellar companion at 16 arcsec 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 micron 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. After integration of the combined spectrophotometric spectral energy distributions, we obtain 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 lay near the past positions of young star clusters like alpha 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 Mjup, close to the frontier between planets and brown dwarfs.