Only display posts after current date

Turns out meta_query was the way to go. This is the code I used to make it work.

add_action( 'pre_get_posts', 'filter_posts' );
function filter_posts( $query ) {
    $now = date("Y-m-d H:i", strtotime('+2 hours'));
    if( is_category() && !is_admin() && $query->is_main_query() ) {
        $query->set( 'posts_per_page','10' );
        $query->set( 'orderby','meta_value_num' );
        $query->set( 'meta_key','date-start-custom' );
        $query->set( 'meta_query', array(
            array(
                'key' => 'date-start-custom',
                'compare' => '>=',
                'value' => $now,
                'type' => 'DATE'
            )
        ));
        $query->set( 'order','ASC' );
    }
     return $query;
}