The short answer is no. If your equipment is sized correctly for the size of the house it takes all rooms into consideration. You can close them slightly so to decrease a little bit of the air but if you shut them off completely you will cut down the air flow. This can lead to a variety of problems including causing your AC unit to freeze up, the blower motor to go out, and generally your unit running more frequently which wears it out quicker. We recommend running your blower in the “on” position to help mix your air and even out you whole home. If you have an older furnace with a standard efficiency motor we recommend upgrading your furnace to a high efficiency blow motor.
The best way to deal with a dry house is to install a whole house humidifier. We sell Aprilaire and Honeywell Whole House Humidifiers. They attached right to your duct work to keep you comfortable all year long.
Most Manufactures recommend you drain your water heater annually to help flush out any minerals that have settle in the bottom of the tank.