How can seasonal changes affect predator and prey?

Answer 1

In times like winter, some animals may be hibernating, and in other seasons they may be migrating. If the predator's prey is gone, than the species might slowly die off from lack of food. The prey's population would then increase. It is a balancing act.

Answer 2

They would effect them quite drastically, for example in Africa when it is drought season, Lions will have to move north to the source of the river (as the prey does); because if they do not they will starve to death because only a few stragglers of said prey will be left behind and it will not be enough to feed a clan. It usually takes a few months for the "wet season" to set in, but due to climate change the duration between these two (drought season and wet season) is growing longer, i.e if drought lasted 3 months and rain season for 4 months, this overtime would develop to say +1 month each. We are partly to blame, wouldn't be surprised if we saw a large number of animals becoming extinct in the near future.