This is called the "Play" feature, in which is only available for Premium users.
"When returning from a hunt, your hunting party joyfully greets the pack. They will have an option to play with pack members and have a random chance at earning Play Points. Each time your wolf earns 25 play points they can redeem them for Character Points. There are 6 different play options and your wolves will unlock them as they gather play points. For each 25 play points they earn they will go up a level and earn a new Play option. In order to be able to play, you must use up all of your explore moves. If your wolves abandon the hunt from injury/hunger/thirst/etc it won't count."
Winter Month: 3 
Night 
Clear Moon: 
