I worked a few month ago on our customer portal and my partner said it was impossible to make assets custom field visible for user who are not logged on the portal.
I tried again today and did not find a way to get our custom field visible for unlogged user.
So here is the view when you are logged (custom field is "Applications"):

Here is the view when you are as a guest :

As you can see, the field "Applications" disappear.
I tried many things, on the customer permissions but doesn't seems to come from there.
I also tried to change some settings on the custom field like the scheme that apply.
I maybe though it comes because guest user can't access our Assets or maybe it is impossible to make Assets fields visible for unlogged user.