For a winch I would DEFINITELY Hardwire! The plug's prongs that slide into the pinch contacts in the J-1900 box can't carry much current over 20 Amps so I would use a larger size cable (2 to 4ga; depending on the winch rating) and use proper wire bugs to connect between cable junctions; that's not even weather proof! 'Best to you'
Yea, that looks pretty hokey! Can't see how the wires get into the outlet box, or what size they are; but I can see future issues with moisture on the front side. Yea, max current for a standard outlet is 20A.