The nice thing about using a relay (as has been noted) is that the amperage for the horn or headlights runs from the battery to the relay to the device and to ground.
The more direct the path, the better voltage delivered to the device.
If the amps have to go through the ignition switch, the headlight switch, all the wires and finally the headlights, each connection (ignition, headlight switch, etc.) has some voltage drop and the headlights themselves will see less than the 6 volts EMF from the battery.
In addition, each voltage drop is due to the resistance of the device or connection (maybe just a little bit), but resistance produces heat, and heat, well, go figure.
The downside of a relay is the potential for the relay failure. If the relay fails open, well, then no headlights or horn. But if the relay falis and closes, the headlights or horn will blast away until the battery runa down, and as the battery runs low on producing EMF (voltage), the amperage will increase trying to keep the device working, and the heat problem occurs for a whole 'nother reason.
Relays are a good idea, but they do have drawbacks too.
