I am having low pressure/volume when I turn on the hot water, especially in the shower, the kitchen sink, and the dishwasher. I do have some galvanized pipe, but this problem came on suddenly this winter. Could the hot water heater have anything to do with this? It is 14 years old. Is there any way to clean out galvanized pipe?

First off, do you flush your heater out on a regular maintenance schedule? If not then you have mineral build up the hot water pipes.
For long life and fewer troubles you should keep your heater clear of mineral build-up by flushing on a regular schedule. Let me show you how. Attach a hose to the boiler drain at the bottom of the tank. With the pressure on, open the boiler drain and let it run until the water runs clear. You will see a spurt of red,(rust) followed by white grains,(lime or calcium carbonate). This shouldn't take more then a few minutes. Do this monthly to keep it clear. Now flush out your hot water lines on ALL fixtures. Now pull each aerator and clean the screens. Be sure you put them back togather the same way you took them out. Don't forget to flush it out every month. Your heater will thank you for it. The average life of a waterheater is 8 years so you're overdue for a replacement.

We now come to the subject of galvanized pipes. Something I'm familiar with since my house is over 50 years old with the same problem as yours.
Over the years iron oxcide,(rust) builds up in the pipe walls cutting down on the volume the pipe can carry. This shows up every time you turn on mor then one faucet as low pressure. I have see 3/4" galvanized pipe choked down to the diameter of a pencil by iron oxcide. I wish I could tell you that there was a magic solution to this problem. Unfortunately I can't. The only solution to galvanized piping is to replace it and repipe the house plus the galvanized water service. I wish I could be more up beat but old galvanized piping is bad news. Regards, Tom