I've got an F350 that a couple of buddies and I will be taking to WY for the first time in 6 weeks. I added a few critical components to my truck a few years ago that are ideal for this trip.
I grabbed a Warn 16.5TiS winch for cheap off market place. The relays were shot, so I upgraded it to the modern pack.
I added an onboard air system. I highly recommend it.

I added a Ham radio. However, I've never found time to go get my license. It's 1 Saturday a month and it never fails we always have something going on.
I absolutely plan to have my tire patch kit in the tool box and a tow strap. We'll have some basic hand tools. We'll have a shared e-tool with our gear for disposing of human waste and tipi, so that covers the shovel.
I've never bought a NOCO battery jumper, because I knew it would be dead the day I needed it due to just sitting over time. However, after reading this thread it occurred to me it might be a good idea to buy one for this annual trip.
I'm surprised no one said windshield scraper for ice removal. I assume that's standard for your northerners, but not so much for us in the South.
I'm bring a steel plate and spray paint for confirming zeros at elevation if we can find a secluded campsite with a good backstop / mountain side.
I'm going to bring a couple of 5 gal buckets and a little detergent to wash the base layers if we end up in the brush for over a week and don't want to head back to civilization to find a laundry mat. I'm to old for swamp ass.
Edit: I forgot to add that I added a 6X gallon Titan tank to my truck. If that’s not enough fuel we’ve seriously done something wrong.