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 these specifications can be created with
GIMP by choosing to export a TGA, unchecking "RLE compression" and selecting "Origin: Top left". Alternatively,
this script can be used to create the file.
If you want to use the same icon in Steam's game list, add
icon "game"
to the mod's liblist.gam file and make the image 32x32 pixels in size.