Minecraft does not "install" like a usual program (in fact,
Minecraft.exe is not an installer). When started, it creates and uses a folder for itself (
.minecraft), which contains the
*.jar executables and assets, but it doesn't create a new launcher executable that is registered in the OS somewhere.
Minecraft is launched through the
Minecraft.exe file you originally downloaded (and is probably in a
Downloads folder somewhere, or whatever you picked as the download directory), which then runs the
.minecraft/launcher.jar archive in java.
I recommend moving (and, if necessary, downloading again) the
Minecraft.exe to a "safe" directory (say, making a new
Program Data/Mojang/Minecraft directory and placing it there, or moving it to the
.minecraft directory itself) and then making a shortcut to it on the Desktop. Minecraft will not do this on its own, as I described above.