I think it would be fun to use a simplified pioneer game (or a combination of games) to choose either review songs or ways to sing a review song. Any of these games are just fun summertime games too, if you wanted to use the ideas other than for pioneer day.
Pioneer children would have played marbles and you could mark each marble with a number and correlate the numbers to a list of songs or ways to sing. Use thin string to mark a circle on the floor and shoot a marble to scatter the marbles within the circle. Invite a child to select a marble and try to knock it out of the circle with a marble "shooter." Then sing the song associated with that number.
Jack-Straws is another pioneer game which we call pick-up-sticks today. You could write the name of a song or a way to sing a song on the sticks and scatter them on the table top. Invite the children to choose one and pull it out of the pile without shifting any of the other sticks.
Pioneer children may have played I Spy as they walked along the trail. I Spy makes a fun singing time by choosing pictures that correlate with either the theme or with the songs you wish to review. For instance, you could post several pictures including a prophet from the scriptures, Jesus blessing the children, a girl being confirmed, a picture of the church building, Jesus calling his disciples, etc. Choose a child as a helper and ask them to study the pictures and choose something to give clues about. The other children try to guess which picture the first child is looking at. For instance, if the child were looking at a picture of Noah, they might say "I Spy a boat" or "I Spy something large and brown. People are looking at it. They are laughing." When the children guess the object or the picture, sing "Follow the Prophet."
Follow the Leader is another game that pioneer children would have played. Invite a child to think of a rhythmic action that could accompany a review song. Let them demonstrate and have the rest of the children follow while singing the song.
Dancing was a common activity in pioneer times. If you have extra time, it might be fun to do a simple line dance pattern with the kids. Choose one of the songs with 4/4 timing. Have the children spread out just a little. Play the music and review the 4/4 timing by clapping the beat for a few minutes. Then show them a simple pattern like: Right foot-heel, toe, heel, toe. Left foot -heel, toe, heel, toe. Grapevine to the left (step left foot out and step on the first beat, bring the right foot behind the left and shift the weight to it on the second beat, bring the left foot back across the front of the right foot and shift the weight to it on the third beat, then bring the right foot together with the left foot on the 4th beat.) Then do the heel-toe pattern again and grapevine to the right. Repeat for the length of the song. The younger children could just do the heel-toe pattern and clap their hands occasionally. "Follow the Prophet" or "The Church of Jesus Christ" would be fun songs to dance to.
Another fun movement idea comes from the Sharing Time ideas in the July 1998 issue of the Friend magazine. The suggestion is to have the children form a wagon wheel with four children in the middle holding their arms out to make "spokes" and other children in a circle around those four forming the "rim". The children would march as they sing, making the wagon wheel turn. Larger primaries would need to form several wheels.
One more pioneer game that I thought of is Chain Tag. To adapt it to singing time I would start singing and tag a child who would then stand up and sing with me. They would then tag another who stands and joins the singing and tags another, and so on until all the children are singing together.