Half-Life loads the window/taskbar icon from a file called game.tga in the mod folder. It needs to be in Truevision TGA format with a left-top-to-right-bottom pixel order.
An image with those specifications can be created with GIMP
by choosing to export a TGA and selecting "Origin: Top left". Alternatively, this script
can be used to create the file.
In the past, the icon needed to be 16x16 in resolution and uncompressed. This is no longer the case.
If you want to use the same icon in Steam's game list, add
to the mod's liblist.gam file and make the image 32x32 pixels in size.