Here is a frame from the final version of a scene I was animating just recently.
At the start we watch only Sarah as she pushes the tiger's front part. Then Alex comes in, he pushes the tiger's back end. Obviously each push is separate from the other in terms of timing, so the kids don't end up pushing simultaneously. A little tricky to work out against the tiger's body, but the scene turned out ok.
Regarding effects animation for snow foot prints, I originally had planned for a more icy surface with no foot prints. But we ended up doing the opposite instead. Every step in the snow will have contact animation. And there are quite a few sequences in the snow.
Here is the link to a recent post about roughing out this scene: