Unlike Microsoft Outlook, Windows Live Mail doesn't hide itself when you minimize the program; nor does it show its icon in the system tray. The screenshot on the left shows the Outlook 2016 tray icon (once you've enabled the option to minimize Outlook to the tray). But there are several "utilities" (small programs) that add that functionality to Windows Live Mail. The utility I picked, which is the one covered in this tutorial, also works with any other Windows program you want! That's why I picked it: once you're start hiding any minimized program, you'd quickly miss not being able to do the same for everything!
First, go download the RBTray free utility from this page: pick the current version, which as of this writing is version 4.3. Once you click on the link, you'll be redirected to SourceForge, which hosts the actual file. RBTray works on any recent version of Windows, from Vista and Windows 7, to Windows 8 / 8.1 (Pro Edition only), and any desktop edition of Windows 10. Save the zip file to your desktop. Once the download has finished, either click on the Open button, or double-click the zip file ("compressed folder") on your desktop. It contains three folders and two files.
Open the 32-bit or 64-bit folder, based on your CPU and operating system. If you're unsure, go with the 32-bit folder! If you want to know, see this tutorial. Copy the two files from that folder and paste them in another folder of your choice. Ideally, an easy-to-access folder, so that you can quickly launch RBTray. To run RBTray, double-click on the "RBTray.exe" file (depending on your file extension settings, you may not see the .exe - that's ok). Visually, nothing will happen, but the utility will be running in the background.
Tip: if you want RBTray to always run, just make it automatically start with Windows: automatically launch programs on startup. If you paste those two files in your startup folder, you won't need to remember to launch RBTray!
When RBTray is running, you can minimize to the tray any program that has a minimize button. Once you get used to it, you'll never want to go back not using it! To minimize Windows Live Mail to the tray, right-click on the minimize button. As soon as you do, its taskbar button disappears. But Windows Live Mail is still running: you'll see its icon in the system tray ("notification area") of the taskbar, next to the system clock, like this: 
Depending on your current operating system settings, Windows Live Mail's icon when it's minimized-to-tray, might be automatically hidden along with other presumed inactive icons. But Windows lets you control which icons should be visible in the tray, next to the system clock. Here's a detailed tutorial on showing Windows Live Mail's icon, for Windows 10, Windows 7, and Vista. Here's the gist. Click on the up arrow button, click Customize, pick "Show icon and notifications", and click OK: 
To restore Windows Live Mail to the foreground, just double-click on its icon. You can also right-click on its icon and choose "Restore Window" from the menu. Here too, this works the same way for any program you've hidden by minimizing it: 
Note: just because you installed RBTray doesn't mean that you have to minimize everything to the notification area. When you give a program's minimize button a normal (left) click, it will minimize itself to the taskbar, just like before!