The passing of any pet can be hard. But when it is one that has been a constant companion, one that you enjoy spendiing time with. It is even harder. When I ride it's a time to escape the rest of the world, just me and the horse. My horse knows things I would never share with anyone else.
To lose a friend or confident like that, whether expected or not, is hard. I don't think there is an easy way to go through it. You just have to let yourself go through the grieving process. For some that's easier than for others and it takes some longer than others.