I didn't read the other replies, so forgive if anything is repetitive. I'm from FL and have been out west 2x.
Mule deer aren't rocket science - you have a background in whitetails that you can apply for muleys. There are similarities. Find the food, find the deer. The deer move early and late - which is when you should be glassing for them. Look for tracks and water. Don't be afraid to park yourself up on a cliff and watch an area with tracks, etc.
So, you get your permit and head out with your trusty 308 - just use the 308. 150 gr bullet is more than enough for a muley. Bring a shooting stick. I shot a 160-inch on my first DIY hunt with a 100 gr 243 bullet. 300-400 yds seems to be a decent max distance. My buck was 220 yards - I was seated on ground, gun up on stick, elbows on knees - steady as a rock. Get a rangefinder if you don't have one already...
I woulda told you a bunch of stuff about glass a couple of years ago. I had $500+ glass and my buddies got $175 binoculars (Leupold McKenzies I think) (10x40mm binoculars). The deer were easier to see with their binoculars. Then I got a Vortex Diamondback scope for a 350 Legend and while it isn't my Leica ER (on the 243), it is good enough for what I do day to day and is good for legal shooting times. Diamondback isn't a bad glass
So get a pair of 10x binoculars. Use em from daylight til about 0900 and from 3 pm til dark. Be where you need to be before daylight! See where the deer are. If you see nothing in 1 day, move. Midday, the deer are bedded and you can still hunt canyons and timber or go scout for tracks & sign - just don't mess up your glassing areas.
We spent 4 or 5 days hunting the hills, valleys, canyons, etc., saw a 2x2 and maybe 12 does for our efforts. Buddy seen a big whitetail buck and does while watching a canyon with a water source. Pretty much, we found it and he camped out on a ridge while I was standing on a finger ridge somewhere else - both of us seen deer, just no muley bucks.
Turned out the deer were in the sage brush. After that was figured, we saw lotsa deer. Think it was day 4 I saw a handful and buddy 300 yds over a ridge saw the motherload including the buck I ultimately shot. Day 5 it snowed and we did our own things - sat in an area that evening and had 2 does and 2x2 walk up to us. Day 6 we went out for evening hunt, set up 200 yds apart. I watched a herd of deer walk across a hillside and turn to feed about 600 yds out front. They got spooked by something and moved to 400 yds, then again to 200. Shot him at 220. Buddy who was 200 yds behind me did not see a deer at all - crazy how the folds in the land hide stuff. Day 7 he had a gorgeous 3x3 at 150 yds but didn't connect. Day 8 He same on a 2x2 at 80-100 yds and called it a fun trip. He didn't want to hunt day 9 and be rushing around for check station stuff the morning of his flight on day 10. Was it dumb luck? Not exactly, but we coulda done better if we had glassed more. Just kept covering ground looking for deer or sign.
I have a big pack and used it cause everyone said you have to. Got tired of lugging it around and used a lumbar pack I prefer - will leave big pack at home from here on out. Tailor your stuff to where you are hunting and how far you'll be from the truck at sundown. If you feel better setting up camp you'll need a fire starter and a smaller tarp - I think mine is 5x7. Used it in the rain once. Very handy.
Boots. You'll be walking a bit - 800 seems heavy but maybe you'll be there late season. I run 400 gr with cabelas ultimax socks. Has been good to me. Get a comfy boot with good support.
I found layers to be more important than jackets and stuff - a breathable raincoat is my outer layer. Fleece and synthetic or wool long johns beneath that. Good gloves, beanie for head. I did carry a change of socks but never changed em.
That's about it. Take my stuff with a grain of salt.
Did an antelope hunt and found a nice muley buck, shot 2 speed goats. Did the muley hunt in a diff state and found some deer. If I can do it, it's not rocket science. Find the food sources, find the deer. Practice w your rifle enough so that you won't miss any shots and go have fun.
Good luck.