It depends on how you are going to set it up. If you're syncing an "isMoving" instance boolean variable.
For all the peers and host:
+ PlayerObject: [X] Is isMoving
-> PlayerObject: Set animation to "Idle" (play from beginning)
+ PlayerObject: Is isMoving
-> PlayerObject: Set animation to "Walk" (play from beginning)
Then all you need is for the host to properly toggle the isMoving variable for each peer when they are moving or not.