Half-Life loads the window/taskbar icon from a file called game.tga in your mod folder. It should be 32x32 in size, Truevision TGA, uncompressed. It needs to have a top-left-to-bottom-right row-major 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.