Last fall I planted three different cover crops - winter rye, oats and clover. They have different characteristics. Winter rye - shown here - survives the winter and grows quite thickly. The patch shown here was something of a disappointment because the winter rye did not germinate in most of the places where I planted it. In fact, I went out and bought more seed because I thought the seed from the previous year was not viable. Last year it had grown very well. Rye does not fix nitrogen but it obviously holds the soil in place. It needs to be dug under in the spring and allowed to break down before planting in those areas.
One of the other cover crops I tried was oats. Oats are not winter hardy as can be seen from the thin dry layer of oat remains in this photo. The soil surface is protected and the dried up oats can be lifted off and added to the compost pile, leaving a nice surface for planting this year's crops. Oats don't add organic matter or nitrogen to the soil.
The third cover crop I tried was clover. I don't recall whether it was red clover or white clover - I had only written "clover" on the bag. I had used clover during the growing season last year in among the kale to reduce weeds. I suppose that is like choosing clover as your weed and using it to block out other weeds.
I thought I had read that clover did not survive the winter but clearly that wasn't true for what I planted. Now it needs to be dug under so that what grows in this bed during this year is what I want to eat and not more clover. Time will tell if I have introduced a new weed to my garden. I assume that since the clover has not been allowed to go to seed that it will not be a problem.
Using and learning about cover crops is one of the items I had put off until I retired.