Restriction - yes. "Problem" - depends on your perspective.URL open failed: failed to open stream: no suitable wrapper could be found
Does this mean it's a problem with my hosting service?
I would say there is a problem because there really is no reason why a PHP should not be able to open a URL.
However, this will only stop your templates from working if you use $TEMPLATEURL in FormMail.
If you use $TEMPLATEDIR, instead, specifying a directory (a directory doesn't being with "http:", BTW), then templates should work.
Use the http://www.yourdomain/formmail.php?testalert=1 feature to find our the correct directory path for your document root (and, hence, your template directory).