New Lawn gone wrong
 

I had a new lawn laid in October (Turf). I didn't do anything to it and it seemed to take root. However after the first frost, the grass went flat. It always seemed to be wet so I didn't cut it. Then squirrels and various nocturnal animals constantly walked on it. Now I have a patchwork of brown and green and alot of the turfs don't seem to have
taken root,

What I should do?

Should I cut it? Should I wait til Spring and cut it? Should I rake it

I'd be most grateful for advice