If you’re leaving them outside and your winters are wet and snowy, I’d cover them. Covers would also keep out stray seeds, squirrels that bury nuts, etc. I keep pots like that uncovered in my shed or garage over winter. You’d be surprised how little they dry out... but they’re basically frozen all winter.

Another reason to cover is to avoid breaking the pot. Lots of water in the pot will expand when frozen!

The advisability of holding over used potting soil depends a lot on the quality of the soil to begin with. Generally, it is not recommended if using a standard, widely available commercial mix. Most of these are peat based and generally do not hold up well with the amount of watering containers require in summer and begin to compress and collapse and lose porosity and good drainage.

At the very least, I'd follow LoneJack's methods. Empty any containers and clean and store for the winter. Put the used soil in waterproof containers (I also use big, lidded plastic totes for this purpose) and reuse in spring with at least a 50% addition of fresh potting mix.

I sift my used potting soil with a wire trash can. Then store outside in large (like tree size) containers that I cover with a giant saucer or trashcan lid. The containers have drain holes so there is some air circulation but the lids keep the snow and leaves, etc. out.

I should have added that like LoneJack, I do mix the used with new in the Spring. I usually add a few other amendments to it. I do a lot of containers and just couldn't bear the thought of tossing it all at the end of the season. It seemed so wasteful to me. I've not had any issues with reuse and recycle.

if you leave the soil filled pot outside, turn the pot on its side so the pot doesn't break with the freeze and thaw

I would add pine bark (1/4 - 1/2 inch) in a ratio of 1 part bark to 2 parts old potting soil.