I was walking around in the marsh and found this huge muskrat hut. But I couldn't see any runs or any sign for that matter, but the water was only 2 inches deep and it is a warm water spring (so it doesn't freeze:). I was wondering if the rats just leave the swallow water in the winter and come back in the summer. Or what do they do?

Whatever they want.

Look for chewings nearby. I believe muskrats do migrate however in warm shallow water they should have a pretty easy life. Shallow is not ideal tho, but adaptation is their strength.

Might have moved, might have been trapped, might have been eaten, might still be there hard to say, look closer might have missed something

not all huts are dens. some are just feeders

I've found a couple of huts in spring areas Iike that and the mink had cleaned them out .
Shallow water and a spring on a frozen marsh is a great location for predators. It would probably be a good location for coon and mink. If you are trapping there already, removing those would be beneficial to the rat population in the future and if there are any rats then you will probably catch some.
Seeing some sort of sign would be encouraging.