A foal is an equine up to one year old; this term is used mainly for horses. More specific terms are colt for a male foal and filly for a female foal, and are used until the horse is three or four. After it has been weaned from its dam, it may be called a "weanling". When a mare is pregnant, she is said to be "in foal". When the mare gives birth, she is "foaling", and the impending birth is usually stated as "to foal".

A baby newborn goat is called a kid.

It's not strange to find a goat with twin kids or even triplets.

A fawn is a young deer that is not weaned and usually under one year of age.

A pony can be of any age or breed. The term pony is used to define any equine that measures 14.2 hands and under. A hand is four inches and is the standard measurement used for horses and ponies. There are many pony breeds around the world but what separates a pony from a horse is height. Typically an official measurement is not done until the age of six years. Horses between weanling and five years of age often measure under 14.2 hands but would not be considered ponies unless they do not grow and stay below the limit when they mature.

More Info: en.m.wikipedia.org