We had an old washing machine in the garage, replaced with a new machine that was moved back into the house, so the plumbing was moved inside the wall to go into the house. We are only getting hot water.

Did you leave a valve closed when the plumbing was extended? Are you getting cold water to the spigot? If so have you checked the inlet screen on the washer, might be enough debris collected its blocked.

Let's do some checking. Remove the cold water hose from the cold water valve and check the screen. Sometimes when you move plumbing you disturb minerals built up the pipe walls. This mineral buildup can clog cartridges, aerators and anything with a screen on it. Let me know what you find. Good luck, Tom