You are setting the cookie on the client which occurs after the page loads and the server code has run once. Since it appears you need to use javascript to check the country, you would have to also use javascript instead of php to hide or show the content on this page. Something like:
<body>
<div id="hideorshow" style="display:none;">
<p>test</p>
</div>
<script>
if (geoplugin_countryName() == 'Italy') {
document.cookie = "country=italy";
document.getElementById().style.display = "block";
} else {
document.cookie = "country=other";
}
</script>
</body>
On future pages, after the cookie has been set, you can use the php method to hide or show contents.