The Windows Live Mail client will continue to work with OTHER email services but not with Outlook.com (Hotmail) because Outlook.com will stop supporting the DeltaSync protocol that WLM uses to communicate with it. Even then, you can change WLM to access Outlook.com via IMAP and it will work then.
I am still using WLM 2012 to access my Hotmail account and everything is still working but I suppose it's only a matter of time before it stops working. Once it stops working, I will probably switch to Thunderbird as my email client.