How much clothes should I bring (noob question)

Use duffel bags, gym bags, backpacks, etc. Anything you can break down to a small area. No suitcases.

Realistically ONE week's worth of clothes. There are laundry facilities in the company terminals, and the hotel. Every truckstop has a laundromat (YMMV on their availability).

Like everyone else said, take cold weather clothes. You should know what you need/like for cold weather, but if you've never experienced it in person, go to REI, Big5, Dick's or other sporting goods place and ask what they think would be good for snow boots, gloves, jacket, etc. (Working level stuff, not expensive outdoorsman gear. You don't need North Face overpriced crap).

On the road, you'll get a shower daily or every other day. I ALWAYS got a daily shower with the rarest of exceptions. Laundry you fit in when you can. If you get a nasty trainer that smells bad and never cleans, then you need to ask for a new one. Make sure you have your dispatcher's # and the recruiter or HR # before you leave. When I went through training 17 years ago my 1st trainer was a mess and one phone call had us heading back to the terminal so I could get a new one. The second trainer was a saint and insisted on daily showers and good breaks once a week for laundry. My co-driver and I (after training) sat down and discussed our shower and laundry and cleanliness expectations before we agreed to team up. Don't get bullied into driving with anyone that doesn't make you comfortable. (This of course goes out the window if you, yourself, is a nasty smelly person. Then I guess you won't care too much).

What A21CAV said: You need to have the ability to hump your gear solo. So if you can't carry it all, you've got too much. Training will suck a bit, but remember, you'll get out of training and get to go home to get more gear. You may even get lucky and swing by your house in your own truck. So just bring what you need and worry about the rest later.

Also. 2 pairs of shoes minimum. You're gonna get one wet or muddy and need the other.