Verbs to indicate animals walking?
Native Chinese speaker here.

No, we do not have many specific animal locomotion words in Chinese. You can very well say they 'walk'. 
But, when we want to sound learned or create variation, we do have more descriptive vocabularies for movements. These words are applicable to the movements of animals, human, as well as objects sometimes. I can give you some examples.

dash - 冲 (横冲直撞 can describe a wild person or animal running around frantically); 

measured steps - 踱着方步 or 踱步 (can be used to describe the canter of a horse);

cat walk - 猫步;

横行 - it is the walk a proud person or a crab;

limping- 跛足而行，跛行;

潜行 - moving stealthily under water or in the dark;

滑行 - gliding on land or in the air;

扑 - jump of a tiger, lion, etc. (any predator)

三步并作两步，连滚带爬，上蹿下跳 are more complicated modes of movement.