All my potted citrus plants are now outside in open air. During the last couple of days we've had a lot of rain here. Because of this, all pots are now soaking-wet.

Should I cover the pots to protect the soil from any more rain, or should I not worry about this? Of course I could also bring the plants inside again, but the inside location where I normally put the plants is now darkened to keep the sun warmth out (when it's there).

This probably all depends on the soil mix you used. What are the citrus growing in?

Some are planted in the soil that I wrote about in this post:
link

The others are still planted in the soil they came in, of an unknown composition...

If the root zones have high levels of aeration, with oxygen available to the root systems, then the amount of water, no matter how much, will not hurt the trees. If the growth medium has compacted, with minimal aeration, then over watering can be a real killer. Remember, it is not the amount of water, it is the the lack of root zone oxygen that does the damage. - Millet ((949-)

That is a common occurance here along the central Gulf Coast--we just came thru a period of heavy rain every day for over a week. It never affects my container trees with the chunky pine bark media. I do have to water a little more often now that they are larger trees--once every 3 to 4 days in the summer.

Well the heavy rains have stopped now, so I can stop worrying!