Just get large freezer storage bags that zip closed for small things. For an entire pannier full use a gabage bag that is big enough. Don't cover the top of the pannniers, just drop in a load in a sealed garbage bag. Clear bags make it easy to find something. You can use a 30 gallon trash bag as an emergency rain coat too. Cut a hole in the top and two on the sides for your arms. It works great. You can easily carry an extra bag folded up for a raincoat, or, a replacement if you rip the ones covering the load in the pannier.
Non zip up sandwich bags that fold over the sandwich, not the zip up type, make a great windbreak over your socks and inside your shoes. If you have thick enough sock insulation the bag adds warmth. Extend the long flap of the foldover sandwich bag up and over the top of your foot, for better coverage. If you get caught in a down pour, the plastic bags from the Supermarket over your shoes, and taped with anything, even scotch tape will keep your feet a little dryer and also, a little warmer in the cold.

Plastic bags work better than heavy covers or bags. The price is right and they are lighter.