It is my understanding that in a web
environment, connections are pooled
automatically. It is also my
understanding that in a Windows app,
this is not the case.
No, this is wrong, as m3rLinEz pointed out. Connections are always pooled.
Therefore, for a Windows app, the same
connection should be used and not
closed after each call, but instead
closed when the app shuts down.
You could keep a connection open for the duration of the application in a monolithic WinForms app. But it's better to use the standard pattern of opening/closing connections whenever you need them. Connection pooling means you won't notice a performance difference. And your data access code will be compatible with server applications such as ASP.NET.
If it is, can two threads use the same
connection to get a dataset from the
DB at the same time or is that
functionality queued up?
No. The ADO.NET classes (connection, command etc) are not thread-safe and should not be shared between threads without synchronisation. But as noted above, you should prefer the standard pattern for data access.