Answer: As you correctly noted, Canada geese (and swans) do mate for life. Mated pairs not only raise and protect their young together, but also look out for one another over the course of their lives. One mate will stay by the other's side if injured or dying, even if the rest of the flock is moving on. They are extremely devoted to one another.
It is certainly possible that when one goose dies, the survivor will find a new partner. However, as with people, every goose is different. Whether or not a goose decides to pursue a new mate involves a number of factors, many of which we don't fully understand. Members of pair that have been together for many years are probably less likely to take a new mate than had the situation involved a younger pair -- but it is still up to the individual bird.
Canada geese are very social creatures, so the lone goose will always have a flock to be associated with when he or she chooses to socialize again. (Sometimes geese in mourning will stay by themselves.) It is possible that the goose will become a loner, but it is impossible to generalize. Again, it depends on the specific goose's "personality."
Question: If one goose of a mated pair dies, does the mate mourn? A goose on our lake died yesterday and last night and all this morning, his mate has been swimming around the lake calling out in what sounds like despair. It is a loud sad short honk, and he/she just keeps circling the lake doing this.
Answer: Those who have spent time observing geese will tell you that they are, indeed, very emotional creatures. There is little doubt that geese deeply mourn not only the loss of their mates, but also the destruction of their eggs. The behavior you observed is most certainly what one would expect of a mourning goose. It is hard to say exactly how long they mourn; certainly, longer over the loss of a mate than for the loss of eggs. Geese in mourning will often stay by themselves for a while.
To me, the Trumpeter Swan is one of the loveliest creatures. Compared to Canadian geese the swan is larger with pale plumage. Geese have shorter necks and longer legs. A swan's bill is twice the length of a Canada goose's bill. They sound the same. Sort of. Being migratory birds, they all fly in a V.
Still, there is something so graceful about the pure white bird. Swan. Even the name evokes a gentleness. You think ballet. Poetic. Love.
Listen to the *calls* of the Trumpeter Swan.
Just like the geese that I wait for, they too sound a lot like spring.