I'd be sort of surprised to find an NSView / NSControl hiding mechanism available in AppleScript Studio, since it isn't available via Obj-C or Java. NeXT/Apple never implemented it because controls that hide and show themselves are generally a Bad Thing in Human Interface terms. (Granted, there are several legitimate applications for hiding controls, but not near as many as developers tend to think.)
If it's a non-editable text field (that is, a non-bordered label) you want to hide, consider just setting its stringValue to @"". If it's an edit field, why not just disable it? Then it won't surprise the user by appearing and disappearing unexpectedly.
However, this is a frequently asked question in Cocoa developer circles, and as such, there are a few common ways to tackle the problem.
The simplest is to use -removeFromSuperview on the NSView you want to hide. Since removing a view from the hierarchy releases it, you'll want to make sure you retain it first so it doesn't get deallocated before you want to show it again (by using -addSubview

. This doesn't work so well for auto-resizing of views and subviews, though, since your view will come back in with its old frame when you add it back again.
Another way that's been suggested is to create a trivial subclass of NSView which implements hiding by overriding -drawRect: to be a no-op whenever the view is supposed to be hidden. Make the subclass poseAs: NSView, and you can then hide any view or control. Of course, writing a posing subclass has to be careful work...
As for the fading: I believe if you look in the open-source OmniAppKit framework (available from our web site) you'll find some code for fading views in and out when adding or removing them from the view hierarchy.