I'm not sure there is an option to do this immediately. Also, this probably depends on your setup.
For gmail, if you use IMAP, there selections under "Mailbox Behaviors" that determines this. Specifically, the "Trash" section offers:
__ Move deleted message to the Trash mailbox
__ Store deleted messages on the server
Permanently erase deleted messages when: <timeframe>
where <timeframe> can be "upon exit"
I'm not sure about the Hotmail. If you can use IMAP instead of POP it is recommended.