This paper considers a multiple-input multiple-output (MIMO) wireless system wherein two legitimate users attempt to exchange secret keys over free-space optical (FSO) channels. Novel frameworks for the use of the one- and two-way discrete-variable quantum key distribution (DV-QKD) protocols, employing weak coherent pulses and decoy states, are presented. Focusing on the case where a photon-number-splitting attack is adopted by the eavesdropper and the legitimate multi-antenna receiver using threshold detection for the key extraction, novel expressions for the secret key rate and quantum bit error rate for both one- and two-way protocols are derived. The performance gain with larger MIMO configurations and the tradeoff between the performances with the one- and the two-way protocols with respect to the transmission distance of the legitimate FSO link are numerically assessed.