I found the fix for this on another site:
Internet Explorer shuts down sending email from hotmail. BING tool bar - Microsoft Answers
What I found was that it is the Silverlight add-on is the problem. I had the same exact symptoms as described... that as soon as I went to send a new e-mail, my hotmail would lock up the browser and it would shutdown. It also affect the other browsers on my computer like mozilla.
Use the Manage Add-ons tool to disable the Silverlight add-on.
a. Open Internet Explorer.
b. Click Tools, and then click Manage Add-ons.
c. On the Show drop-down menu, select All add-ons to display all add-ons that are installed on the computer.
d. For each item in this list, select the add-on (Silverlight), and then click Disable in the Information window.
e. Exit and then restart Internet Explorer.
This fixed the problem for me.