DefinitelyDressage.com

Since I stopped riding dressage, about 8 months ago, I have recently started lessons in Western.
My posture has left town.
I used to sit tall and correct, now my very patient instructor has to keep reminding me not to roll my shoulders in, etc.
I feel like a slouch. Is this because I'm riding in a Western saddle now vs a deep seat dressage saddle?

Sorry to say but no. A western saddle may not allow you to get into the same ear-shoulder-hip-ankle alignment but it shouldn't affect your posture from the waist up. Unless your saddle is causing you to roll your butt under and round your back.
You're going to have to concentrate again on shoulders over hips, no chair seat, shoulder blades tucked into your back pockets, shoulders down or elbows down or whatever works for you, hands pushing forward. All the usual stuff.

Could it be originating from your hip flexibility? Western saddles tend to ride pretty wide, so I could see that if you are trying to keep your leg under, other parts of your posture and alignment might suffer if you don't have the hip flexibility to really sit into a wider saddle. Of course not all western saddles are created equally, so it might be worth trying something different if you can.

Western saddles very a LOT. What kind of saddle are you riding in? Brand/model? I ride in a Continental reiner, which is made by some German folks, and thusly allows what I think of as a much more correct position while still being a traditional western saddle and not as weird as I think some of the made for western/cowboys dressage saddles are, at least in my opinion.