With all taps off in the house, look at the water meter, note the reading, then wait an hour or so to see if it moves. You may have a small leak.
The water meter only measures the flow, it does not other function. Not sure what you mean about 'stopped regulating the flow'. There may be a valve near the water meter, and depending on the type and its status, it may no longer turn the water off. This can be a pain, and that valve may need to be replaced. Depending on its location, and how things were plumbed, you may need to get the utility to shut your water off at the street to effect a repair.
Keep in mind that when you shut the water off, the system is still under pressure until you open a valve to relieve it. There still could be a small leak.
Do you get flow from all of your faucets? Did any of them stop during the cold snap? If they did stop, it's likely things froze. That often will cause a leak when the ice melts.