As I'm sure you know, the definite article "the" is used to refer to something specific. So in many contexts, you would say "the cow" about a specific cow, and "a cow" if speaking generally about any particular cow, or a cow you couldn't specifically identify (eg "what's a cow doing in my garden?")
However, we sometimes use the definite article with the name of an animal to refer to the entire species. Just look up any animal species on Wikipedia - for example "The Humpback Whale is a species of baleen whale".
However, while it isn't incorrect to say "the cow" or "the dog" to refer to them as a collective, cows and dogs are not generally spoken of in such terms, possibly because, as domestic animals, they are both broader terms which can be further broken down into different breeds. You are more likely to hear "the Alsatian" or "the Highland" to refer to specific breeds of dogs or cows.