As you've observed, some combinations of -ridden and -infested are more common than others. Shark-ridden is far less common than shark-infested, while both mosquito-ridden and mosquito-infested can be found in literature.
Ridden and infested both indicate an unpleasant excess of something, and could stand alone—
The marsh is ridden with mosquitoes.
The bay is infested with sharks.
— but whether forming a compound or not, there are slight differences.
Infested carries a connotation of being overrun or overcome by a pest or parasite, especially one that swarms: maggot-infested wounds, doily-infested parlors, teenager-infested shopping centers, etc. One can speak of disease in this way, e.g. cholera-infested villages or tumor-infested kidneys, but most non-count nouns do not "infest"; one almost never encounters a angst-infested author.
Ridden, on the other hand, suggest a chronic or endemic condition, especially where the thing in excess is an internal or intrinsic rather than external phenomenon: a slum-ridden neighborhood, cliché-ridden novel, or worry-ridden father. A dog with fleas could be either flea-ridden or flea-infested, but to my ear the former suggests resignation and the latter alarm. Ridden is also more commonly joined with non-count nouns: torment-ridden prisoners and violence-ridden provinces are more common than their torment-infested and violence-infested counterparts.
Of course, certain formulations have become set phrases, or at least more popular than others, and not all conditions can be expressed using one or the other. Waters are always ice-infested or shark-infested, almost never ice-ridden or shark-ridden. On the other hand, one is debt-ridden or guilt-ridden, never debt-infested or guilt-infested. And one is neither age-ridden nor age-infested. As for the pond, it can be either mosquito-ridden or mosquito-infested, so wear plenty of repellent.