Cloud's last ability reduces only the amount of generic mana you pay for equip abilities that target Cloud. For example, it will reduce {2} to {0}, but it will have no effect on an equip cost of {G}.

Some Equipment creature cards in other sets have reconfigure, a different ability that attaches them to a creature. Reconfigure is not an equip ability, and reconfigure costs are not reduced by Cloud's last ability. Equip variants or equip abilities with restrictions, like the "equip legendary creature" ability of Wrecking Ball Arm, are still equip abilities, and their costs will be reduced by Cloud's last ability.