This would work for winter, but would be difficult to theme for summer. We draw a three part, rather large, snowmen on the ground to one side of the bar with a block of chalk, the head furthest from the bar. We do casts from front support, so the snow man is behind them to see who can smash (land on) the snowman's nose. I then will raise the bar and we will swing 3x's and see who can let go and smash the snow man's nose that way. If they are the older 4-5 yr olds, I'll turn them so they let go on the back side of their swing too... underswing dismount prep.
This isn't a game, but it's fun for bars too. Just "discovered" how to use the set up for preschool last week. Doesn't work too well for 2-3 yr olds though, not enough muscle tone yet .
We had the single bar set up with a large mat at a steep incline for beginner clearhip drills for team to start with against the big mat at push up or higher, then drop to clear hip and aim feet as high up the mat as possible. I discovered if you lean a cheese wedge, fat side down, against the same set up the preschoolers could "climb the mountain backwards" as high as they felt comfortable. Some were climbing above pushup, so it would look like the top of a Level 4/Level 5 cast on bars. Pretty good for a preschooler. They then would get to where they could comfortably stand and slide down the rest of the cheese wedge. My kids thought it was great fun, and excellent for that whole body core strength.