This is usually because your email client is blocking images. Hotmail and Yahoo! Mail are two common webmail interfaces which will block the images.
In Hotmail, a message above the forecast email will read:
Attachments, pictures, and links in this message have been blocked for your safety. [Show content]
Click the link which says 'Show content'.
In Yahoo! Mail, a message above the forecast email will read:
This message contains blocked images [Show Images]
Click the 'Show Images' button