I haven't tested this, but this is how I would write it based on what you have provided.

#!/usr/bin/perl
use strict;

# split-logfiles

# you don't need to test if it is open
#$isopen = 0;

my $myfile = "/var/tmp/test.log";

# no reason to do this testing
#    unless($isopen and -f $myfile) {

# open the happy file here, but you may want to use >> if
# you need to append rather then overwrite on each run
open MYHAPPYFILE, ">$myfile" or 
    die "Error opening $myfile";

# don't need to test if it is open because we 
# are dying if it isn't
#      $isopen = 1;
#    }

while (my $log_file = <STDIN>) {
    printf MYHAPPYFILE "%s", $log_line;
}
exit 0;
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And without commments:

#!/usr/bin/perl
use strict;

my $myfile = "/var/tmp/test.log";

open MYHAPPYFILE, ">$myfile" or 
    die "Error opening $myfile";

while (my $log_file = <STDIN>) {
    printf MYHAPPYFILE "%s", $log_line;
}

exit 0;
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