How log of a trail ride will this be?
Is it on your own horse, or will the horse be provided by someone else?
If it's your own horse, be sure your horse is conditioned for that long of a ride. Even "hours" of arena riding, or road riding, is not the same as hours spent on a trail with varied terrain, footing, etc. I've seen horses break down on long trail rides because their owner just assumed the horse would be able to do it because the horse was ridden a lot in an arena or other flat areas.
This past year, I've started using a Zilco headstall that attaches to the halter (works best with narrower halters, or rope halters). It's great because you can remove the headstall/bit when you stop for a long break, and just tie the horse with the halter so that it won't go to scratch its head and possibly damage or break your tack. It's beta material. . .very tough but super easy to clean.
Speaking of tack damage/breaks. . .bring along some leather string, latigo, maybe some spare Chicago screws if your tack uses them. . .just in case you DO need to do an on-the-trail repair. Maybe a hole punch as well. Definitely some kind of utility knife/tool, like a Swiss Army or Leatherman. Consider a little folding saw or pruners if you encounter an section of trail that is blocked by overgrowth or a fallen tree. It won't get you through a big tree trunk but it can help through the little stuff.
You mentioned that there will be mud - be sure your horse is also conditioned for that kind of riding. Some of our local parks get VERY muddy. . .lots of clay, and when it rains the water just sits on top. It can be really hard on the horse's legs, especially if they're not used to it. If the horse is shod, be sure there aren't any loose shoes. Might want to hold off on using any horse boots if the horse is barefoot, because muddy trail just sucks those boots right off.
For yourself. . .bring things like a rain coat/slicker, helmet or hat, bug repellent, appropriate clothing and footwear, gloves. Some kind of snack and beverages - I try to avoid anything carbonated or sugary when I ride. Be prepared to "pack out" whatever you bring with you.
"Parelli horsemanship is just like painting by the numbers. You need absolutely no skill. You just put this color here and this color there, and when you're done, you have ... a mess no one wants." mp