So they shouldn't be cached just because of recreating the window, or as I
mention below, does it hold onto a scarce resource (DC?)?  I think someone
indicated a third party control library which caches the Graphics object and
re-caches (lets go of the current one and caches a new one) it each time the
window is resized.  Someone else pointed me to:

http://msdn.microsoft.com/chats/transcripts/vstudio/vstudio_062602.aspx

which contains:

PeterG_MS
Q: Regarding overhead of passing objects to event handlers (such as
Graphics). There's more overhead than passing a pointer. The object must be
created and initialized. For every event, that seems like it would be a lot
of overhead. No?

PeterG_MS
A: Creating a Graphics object would have some significant overhead -- I
don't really know how much. But just passing a Graphics object has little
cost. So one way to improve performance would be a cache a Graphics object
and pass the same way on each event invocation, if possible.

I would rather stay away from caching the graphics object if possible.  
Again my assumption is that if it's expensive to create the graphics object
and there is no harm in caching it the underlying framework (Windows / .NET)
would have cached it for us.