this will be very tricky. First i would create a new product attribute f.e. called only_user, this should be a general attribute.
Than you have to customize all phtml files which lists the products. For example list.phtml of module catalog in the grid mode:
if($_product->getOnlyUser() && $this->helper('customer')->isLoggedIn() )
//Show the product
But theres a problem in grid layout of list.phtml. The whole sum of products is count
If you use above code you have to customize some more code of this function.
<?php $_collectionSize = $_productCollection->count() ?>
Hope you understand my bad english.