How to query expire time with post meta?

You would need to use the function get_post_meta :
http://codex.wordpress.org/Function_Reference/get_post_meta

Something like this:

<?php
$is_expired = get_post_meta($post->ID, 'expire_time');
if($is_expired < strtotime("now")) {
 // your code
}
?>

You need to put your post_meta expire_time into a comparable format.