The relevant passage of perlform is

Inside of an expression, the whitespace characters \n, \t and \f are c
+onsidered to be equivalent to a single space. Thus, you could think o
+f this filter being applied to each value in the format:

 $value =~ tr/\n\t\f/ /;

The remaining whitespace character, \r, forces the printing of a new l
+ine if allowed by the picture line.
[download]

You can achieve the output you want by translating the \n's to \r's

#!/bin/env perl -w
use strict;

my $cookie="Climb the mountains\nand get their good tidings.\nNature's
+ peace will flow into you\nas sunshine flows into trees.\n";
my $author="-John Muir\n";
$cookie =~ tr[\n][\r];
$: = "- ";
format STDOUT =
        @|||||||||||||||||||||||||||||||||||||||||||||||||
        "------------------------------------------------"
~~     ^<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
        $cookie
        @||||||||||||||||||||||||||||||||||||||||||||
        $author
        @|||||||||||||||||||||||||||||||||||||||||||||||||
        "------------------------------------------------"
.
write STDOUT;
__END__
         ------------------------------------------------
       Climb the mountains
       and get their good tidings.
       Nature's peace will flow into you
       as sunshine flows into trees.
                         -John Muir
         ------------------------------------------------
[download]

Though a couple of other adjustments are required.