Ireland doesn't have any native snakes (yet).
Most English speakers wouldn't be talking about sharing mice at all! But there's nothing wrong with this sentence (from a grammatical sense, anyway). We could be talking about mice in general. For example, if your children have a bunch of mice as pets,and someone us offering you another one, you might say "We have our share if mice, thank you." In this case, a specific group of mice aren't being talked about, so you wouldn't use "the".