How do I know when evaporative/swamp cooler pads should be replaced?
You're going to be up there at least twice a year, to put on and remove the jacket, so check the state of the pads each time.

You won't need to replace them every year, but treat them like any filter - if it looks dirty or clogged, it probably needs replacing.

The pads in your photo don't look bad - I'd leave them for now, and check again in Spring.