A manx cat
A common small brown furry animal without a tail is the mouse. Mice are known for their small size, brown fur, and absence of a visible tail.
the animal with small ears but is large is a hourse with its small ears and long tail
a mole
A Squirrel.
All hamsters have tails, however the tail of a Syrian hamster is short, and might be hidden if the hamster is a long-haired one.
A grasshopper
There are several different terms for a short tail, and they all mean the same thing, but the method of arriving at the short tail might be what is different. Bobtail is a short or shortened tail for either a cat, horse, dog, or other animal. To be born that way or to cut it short. "Bobtailed". Manx cat has an internal vestigial tail. Nickname "manxtail".
Elephant.
There are many small animals that are white with a black nose and tail in New Hampshire. This could be a rat.
The snake is an animal that has no tail.
It could be a red squirrel, which is a small squirrel species found in Michigan and has a long fluffy tail. Another possibility is a chipmunk, which is also small and has a long fluffy tail. Both of these animals are commonly spotted in Michigan.
Grebes are small water birds similar to ducks. They do have a tail, but it is very short and stubby and not obvious when you look at these birds.