.htaccess redirect to subdomain not working

Question

I have following code in my .htaccess file located in root of site.com:

RewriteEngine on
RewriteBase /
RewriteCond %{HTTP_HOST} ^(www\.)?site\.com$
RewriteRule ^files(.*)$ http://files.site.com/$1 [L,R=301,QSA]

I want to redirect site.com/files/path?query to files.site.com/path?query, but for some reason it won't work. Can someone tell me why?