Actually, there is a once a year blessing (from the third category) on the blossoming trees. In that blessing we include all creatures. There is no specific blessing thanking for animals since there is no starting point. Upon waking up, however, there is a blessing for giving the rooster the capacity to discern day from night. This is because it is a specific point that we derived a benefit from the animal. On the other hand, even in times when we depended on horses and cattle there was no designated blessing of thanks for them.
As to the other meaning of blessing, to bless a person, when a person is blessed his property is blessed. You don’t have to separately bless his belongings. You can enumerate, as the Torah does, that your children should be blessed and your animal and fields should be blesssed. This is not the same as blessing them. It is a blessing on you about them.