A popular request is the ability to share Exchange calendars with users outside the network. Normally, the only people who can see your calendar are the people you share it it and outsiders won't have permissions. This means you either need to publish the calendar in a more public area when you, the user, can control who has permission to see your calendar, or use Free/Busy. Either way, you should confirm with your administrator that it's OK to share this information with outside users.
Note: Office 365 Exchange users can publish their calendars and make them available to other users. Additionally, Outlook users can send a copy of their calendar (as an .ics file) to other users.
We have Exchange 2007 SP2. I have a public calendar that I would like to share to our customers through our website. I don't want to publish with Office Online and WebDav because customers must have Outlook to open it. I'd like to send a link to customers to connect with HTTP and open the calendar in OWA.
First, I'm going to address the misconception that Outlook is required to view calendar published to Office Online or WebDav servers. They will need to use a calendaring client to view the calendar though, but it can be anything that supports the ical protocol, not Outlook specifically.
If you use Exchange 2010, see Sharing Exchange 2010 Calendars with Outside Users for the instructions to share Free/Busy with customers.
Now on to the question...
While you can do this in Exchange, a SharePoint calendar would be the perfect solution.
In either case, you will need to create accounts in the AD for the users, either generic account for all guests to share or individual accounts. If you use public folders, you'll need to create an account in Exchange, while SharePoint only needs an AD account (unless you give the calendar anonymous access.)
A SharePoint calendar will work equally well in Internet Explorer, Firefox, or Chrome. You can link either SharePoint 2007 or 2010 to your Outlook and create appointments in the local folder which will sync to SharePoint. The customers who have Outlook 2007 or 2010 can link the SharePoint calendar to their Outlook. If you'd like to try a calendar in SharePoint, we have a SharePoint 2010 demo at xsolive.com. SharePoint's default permission is no anonymous access, but our calendar has anonymous access enabled, with view permissions for anonymous users.
If you really want to do this in Exchange server, create a mailbox and set the mailbox quota to 0 so the customers can't send email using it, and then give the account permission to the public folder. Share the acct info and provide users with the URL. To get the URL, open the calendar in OWA and right click on the folder and choose open in new window. Note that the public folder calendar will not work in Chrome or Firefox.