Days before I got a big box large enough for a sunbeam and drew wheels on it with marker - this would be our "wagon" (or you could just use a wagon if you have one, but the kids loved pushing a child around in the box). I collected sticks to make a "campfire" with and brought a blue blanket to be a "river." I also got some paper cups and some pieces of paper that we wadded up into balls for a pioneer game of toss and catch. Then I made a few pioneer button spinners (you can find lots of examples online). I also prepared some snacks, I chose dried apple slices and pretzel sticks.
Following is my plan with dialog and songs to sing. I planned out which corner to do each section in and placed my objects around the room accordingly. The kids know about half of the songs which helps them not feel too uncomfortable when we sing the songs they don't really know. You can play the songs from the Church music app if that helps.
The kids had a lot of fun and remembered the activity for years! It also helped them be interested in Pioneer stories of their own. I told them to go home and ask their parents if they have any pioneer ancestors and to ask them to tell their stories.
You can find my Singing Plan here: Pioneer Day Singing Time