Replying to Driving in utah during the winter- vehicle requirements

Whats up guys so Im an out of state student in slc and im bringing my 03 vw jetta here next week. Its a front wheel drive with 6 speed manual trans. I am confused about the requirements for winter driving in the mountains. From what ive heard if you car does not have 4 wheel drive/ all wheel drive then you have to have snow tires or chains. Is this correct? Also how is driving through the mountains during the winter? Does it get pretty sketchy or do they do a good job with salting and plowing? Just a bit worried cause it will be my first winter with this car. Im from Wisconsin so I do have experience in the snow.