After installing a snap with
gnome-software a “Permissions” button appears near the “Remove” button and you can set permissions for that snap(this reminds me of smartphone apps).
But it should have more informations, at least a link to a page(like Click to understand how Permissions work) explaining how it works or maybe a (?) link on each line with a short description explaining what it does, that show up when you hover the mouse cursor or click on it.
For example the Firefox, the window shows this:
I think that more transparency on how this new feature works will prevent people freaking out about it all over the web. The way this is designed right now will probably concern people that values privacy and will prevent them from using snaps and Ubuntu, more information about how it works would be good for everyone.