Interesting question! DH and I are doing the same thing in October as part of a tour in Jamaica. It didn't even dawn on me to make sure it was something we would be able to easily hand without becoming sore the rest of the trip. Maybe Jennasis will come on here with some advice for us!
Did somebody say my name? haha! hi guys!
Yes, if you are a beginner you will likely be a bit sore after a 2 hour ride, even if it's just a "walking tour". If you'll be doing anything faster than a walk, then the soreness may linger a bit longer/be a little more pronounced. As the others pointed out, Advil should be fine. When I mean sore, I'm talking about your seat bones specifically along with your thighs. You may have some back discomfort too depending on the intensity of the ride, the comfort of the saddle (trail ride places don't usually have top of the line tack) and also how tense you are throughout. The more relaxed you two can stay the better you'll be.
Some tips:
Wear long pants. NO shorts and NO capris. You will end up with horrible chafing/road rash type sores on your inner knee and calf if you wear shorts etc.
Avoid sneakers/tennis shoes if possible. Try to wear something with a small heel (1-2 inches) with a hard sole. Sneakers tend to be too grippy and will not allow you to quickly pull your foot out of the stirrup in an emergency and without a heel it is possible for you foot to slip completely through the stirrup.
If the place offers helmets, USE THEM. I do not ride nor permit any of my students or clients to ride at any time without a helmet. Even if you are just walking you could hit your head on a branch, the horse could spook/bolt/rear/trip/fall etc. All of which would be devastating to you without a helmet. I've seen it happen. Wear a helmet!
Relax, and have fun. The others are right in that most of these trail ride places employ well trained and quiet horses who will for the most part, walk single file, nose-to-tail. Bring a camera and take photos, and a change of clothes for afterwards. Be sure to tell them when you sign up that you are a beginner. Be honest with them so they can match you with an appropriate mount. Have fun!