theres a board spec called waist width which is basically the width of the board in the middle. most boards are 24-26 inches wide. many companies make wide models of their popular boards for people just like you who have rather large feet in relation to their height. a wide board will prevent you from having too much toe or heel over hang. if you have too much over hang your boots could drag in the snow when you turn on your edges causing at minimum to loose speed and at worse to eat shit.
to sum up not all folks with size 13 boots need a wide board.. some one who os 6'4 wont because they will ride a longer board which will naturally have a wider waist width. someone like you who is smaller will of course ride a smaller board which will in genneral have a lesser waist width. thus to avoid overhang issues it may be in your best interest to find a wide board.