If you mean windows Live mail.. Then do this,
Find windows live hotmail in you all programs list or program files and drag that shortcut to the dock.
If you mean the acually hotmail site then this will work...
Go to hotmail.com and when the page is loaded you will see some icon before the adress. Mouse over this icon and a hand will apear as your cursor. Drag the icon directly to an empty space on the dock.
a third option would be to right click the dock and find "this dock" this brings up a submenu and in the menu is an ADD option. You will want to add a new shortcut. When the shortcut is on the dock the icon for it will be that question mark. Click on the icon and a diolog will pop up. This is where you will name the dock entry and configure the shortcut..
For example if you want it to go the hotmail site online you would type hotmail.com as the path.
If you need any additional help do not be affraid to PM me I am very glad to help.
Here are some images to show you what I mean