I checked a ton of forums and none of them had this hint -- only the same questions over and over. I hope I'm not embarrassing myself by stating the obvious. If it hasn't been noticed before, I guess I stumbled across the fix.
Open your iPhone's Safari browser and log in to your Hotmail account. Then, all you have to do is tap the Bookmark button. A screen will come up asking what you would like to do. Simply select Add to Home Screen. You should now see a Hotmail icon up on your home screen, just like an app; it even has its own App icon.
When you select the 'app,' your Hotmail will open up in Safari, automatically refreshing. It will live update, and maintain your folders, including folders you've created.
[robg adds: Microsoft offers this document, which explains how to set up Hotmail as a POP3 client on the iPhone. However, there are downsides to POP3, such as only being able to see your inbox. I'm not sure if there are any better ways to use Hotmail on the iPhone, as I'm not a Hotmail user. Suggestions welcomed in comments.]
Mac OS X Hints
http://hints.macworld.com/article.php?story=20100111125214485