An alternative:

use Algorithm::Loops qw( NestedLoops );

my $source = 'horse:cow:dog:cat';
my @parts = split(/:/, $source);

my $iter = NestedLoops(
   [
      [ 0..$#parts ],
      ( sub { [ $_+1..$#parts ] } ) x $#parts,
   ],
   { OnlyWhen => 1 },
);

my @s;
print(join(':', map $parts[$_], @s), "\n")
   while @s = $iter->();
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Update: Even better:

my $source = 'horse:cow:dog:cat';
my @parts = split(/:/, $source);

for my $comb (1..2**@parts-1) {
   my $s = join ':',
           map $parts[$_],
           grep $comb & (1<<$_),
           0..$#parts;
   print("$s\n");
}
[download]

Update: Neat, and even faster:

my $source = 'horse:cow:dog:cat';

local $_ = ":$source:";

my $parts = tr/:/:/ - 1;

my $re = '(?{ "" })'
       . '(:[^:]*)(?=:)(?{ $^R . $^N })'
       . '(?:.*(:[^:]*)(?=:)(?{ $^R . $^N })' x ($parts-1)
       . ')?' x ($parts-1)
       . '(?{ push @rv, substr($^R, 1) })'
       . '(?!)';
  
{ use re 'eval'; $re = qr/$re/; }

local our @rv;
/$re/;
print "$_\n" foreach @rv;
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