A couple weeks ago, we woke up and there was no water. We assumed that the pipes were frozen and cranked the heat. After a few hours the water was back to normal. Now, suddenly, after being fine for the past 2 weeks, the water is muddy looking. One morning a few days ago, the well cap outside appeared to have ice on it. Could this be related? Is there anything we can do? Is this sediment going to ruin our water heater?

If you are pumping from an artesian well, I would think it would be a simple matter to pull the well cap and eyeball the well to see if the sides had perhaps caved in some and muddied the water. You might also have some sediment built up at the bottom which is being partially pumped.