>perl -wMstrict -le
"my @COUNT = (
   'Family    lacM    taba    mori    glyB    gly4',
   'OG_1    1    0    1    0    0',
   'OG_2    0    1    0    1    0',
   );
 ;;
 my @families = split /\s+/, shift @COUNT;
 ;;
 my %participants;
 for my $record (@COUNT) {
   my @fields = split /\s+/, $record;
   $participants{$fields[0]} =
     [ map { $families[$_] } grep { $fields[$_] } 1 .. $#fields ];
   }
 ;;
 use Data::Dumper;
 print Dumper \%participants;
"
$VAR1 = {
          'OG_2' => [
                      'taba',
                      'glyB'
                    ],
          'OG_1' => [
                      'lacM',
                      'mori'
                    ]
        };
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Update: The expression
    [ map { $families[$_] } grep { $fields[$_] } 1 .. $#fields ]
is more concise and perhaps a bit faster as
    [ map $families[$_], grep $fields[$_], 1 .. $#fields ]