I live in NJ so its cold right now and everytime i start my car in the morning (clutch all the way to the floor tranny in nuetral) i here a weird noise fromthe tranny almost like grinding but not really almost like something is stuck together and their peeling apart the colder it is the worse it gets

is it just the weather orsomething to worry about also until my car warms when i depress the clutch the whole car like shakes

this is my first nissan manual so im wondering if this is normal for nissan's? thanks