Wait a minute here, folks. First of all, according to Genesis, the land animals which crawl on the earth and the birds DO have soul, or 'nephesh.' That is also translated as 'breath of life'. "Nephesh" is used 757 times in the Old Testament. The most common translations of this word are 'life' and 'soul'. However in Genesis 1:30, this same quality is ascribed to 'all the beasts of the earth and all the birds of the air and all the cratures that move on the ground.'
This does NOT answer regarding animals in heaven or not, but it does answer that soul is not the exclusive property of humans. It is in spirit that we are created in the likeness of God. Our bodies have the same elements in them as stars and rocks and trees and butterflies. Unlike all of those, however, we share with the 'more advanced' animals individual personalities, the ability to learn and consciously react, and the ability to forge inter-species relationships. This is part of 'soul.'
It is because of our spirits, however, that we are able to comprehend things we have never experienced, at least to some extent: the distant past, ideas about the distant future, creating something new and unique to the person. It is spirit that allows us to communicate with God Himself on a person to Person basis.
Regarding heaven, well, white horses seem to make it -- grin. That's what Christ comes riding on. And if horses, why not the rest? A new creation is a new creation, not necessarily a limited (more limited) one. We know in the Millennium the lion will lie with the lamb and a child play with a deadly serpent with no harm -- so animals in their original state are certainly a part of the original creation. The new creation will simply be without sin and/or its effects -- or even the memory of it! But that doesn't mean it will be without animals. They don't sin.
Keep in mind that the animals with nephesh were saved on the ARK. The Ark has always been a picture of salvation in Christ. I see no reason, theologically, why animals would not be in heaven also. They have never needed saving in terms of sin, but Christ saw fit to save them from being wiped out with the old world. This may be a picture for us?