Well, generally, packages should keep their hands off of other packages' variables. It's considered unsafe. Instead, you could have (in each subclass) a class-level method which returns a reference to the desired "private" variable. E.g.

package my::model::subclass;

. . .

sub normal_hr { # because it returns a hashref
    \%normal
}

# then:

package my::model;

. . .

sub use_subclass_package_var {
    my ($self, @cols) = @_;
    my $normal = $self->normal_hr;

    foreach my $col (@cols) {
        next unless exists $normal->{$col};

        # the rest of the code
    }
}
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But I'm confused as to what you're really trying to achieve here. My gut instinct is that whatever it is, it's probably better done another way.