What's the best approach? My solution feels a bit clunky...

You could omit a couple of temporary variables and initialising $rating wouldn't go amiss:

my $hdata = <call that creates the struct>;
my ($rating, $bwurl) = 0;
foreach my $id ( keys %$hdata ) {
    if($hdata->{$id}{Season} == $seasonnum && $hdata->{$id}{Rating} > 
+$rating){
         $rating = $hdata->{$id}{Rating};
         $bwurl  = $hdata->{$id}{BannerPath};
    }
}
[download]

But essentially what you have is about as good as it gets.

You might use List::Util::reduce(), but it is certainly no clearer:

use List::Util qw[ reduce ];
...
my $hdata = <call that creates the struct>;
my( $rating, $bwurl ) = @{ reduce{
    if( $hdata->{$b}{Season} == $seasonnum && $hdata->{$b}{Rating} > $
+a->[0] ){
        $a->[0] = $hdata->{$b}{Rating};
        $a->[1] = $hdata->{$b}{BannerPath}
    }
} [ 0, '' ], keys %hdata };
[download]