My first step in your situation would be a soil test. The UC Extension service doesn't perform soil testing, but this pdf has a list of labs in northern and central California. The results of this test will tell you in what ways your soil is deficient.
You don't specifically mention what you're growing, but it sounds like vegetables.
One thing that makes it hard for many vegetables to be able to take up nutrients is acidic soil. If your pH is much below 6, a number of vegetables will have a hard time. You can add lime in the amount recommended by the soil test to bring your pH closer to 6.5-7. Soil that is too alkaline will also be a problem, but I'm less familiar with the symptoms there.
Adding composted horse manure is a good idea. The biggest variable with horse manure is the bedding: does the stable use straw, sawdust, or something else? From one perspective, straw is better because it breaks down faster. From another perspective, sawdust (or any wood product in general) once well rotted, holds an outrageous amount of moisture. Then again, having woody remains in the garden if you get a lot of moisture can lead to mushrooms/toadstools. If wood-based bedding is not well rotted, the decomposing woody material will steal nitrogen from your plants so that it can decompose.
Standard advice is to add about 0.5-1" of compost to poor soil, though I've on occasion added much more than this. (I wrote a calculator to figure out the volume you need to add a given depth of manure to your garden; you may find it helpful.) Work it deeply into the soil -- 6-12" depth is a good goal. You don't want to focus nutrients in the top layer, this encourages plants to develop shallow roots. You also want to put moisture-holding humus into the lower layers of soil.
Another problem you might have is soil compaction. In this case, if the space isn't too large, you're in good shape, and you have the time (several hours per 100 square feet), you might consider double digging:
- Loosen the area with a garden fork.
- Remove weeds.
- Spread your compost/manure over the area to be double-dug.
- Add lime as recommended by soil test.
- Dig a trench as wide as your spade across the width of the bed, to the depth of your spade. Put the soil in a wheelbarrow or buckets -- you'll use it at the end of the process.
- Using the garden fork, loosen the soil at the bottom of the trench to the depth of the fork. While you're working, avoid mixing the soil layers -- you don't want to mix subsoil into your topsoil.
- Move back, dig another trench adjacent to the first one. Put the soil from the second trench into the first trench. Loosen the soil at the bottom of this new trench with the fork.
- Repeat until you come to the end of the bed. Use the soil from the first trench to fill the last trench.
- As you're working (and in the future), don't walk on the garden bed. This compacts the soil. Standard advice is to place a board across the bed to stand on while you're double digging, but I don't see the point -- you're already probably dealing with compacted soil, and you're in the process of fixing the problem anyway. Just don't walk on the areas that have been double dug or you'll undo your work!
"How to Grow More Vegetables" by John Jeavons has a whole chapter devoted to soil prep and double digging.
You said you don't want to build it up to a raised bed, but this process loosens the soil and adds so much air that you will (at least temporarily) raise the garden soil somewhat. You don't need to create formal borders or anything, and the soil will settle over time.
A cover crop that you till into the soil next spring is a great idea. Peas and beans aren't bad, but if you want to generate a lot of biomass (and I think you should want to), I'm a fan of "PVO Mix" -- that's Peas, Vetch, and Oats. I think your winters are fairly mild, so this should do well for you. The main challenge is chopping it all up when it's time to till it under (vetch and peas can get pretty tangled up in the tiller tines). The vetch and peas both play host to nitrogen-fixing bacteria, and the oats grow tall to provide support for them as well as producing biomass. Fedco is my favorite source for seed, they have PVO, and I think they're still shipping cover crop seed this time of year. But you can probably find a supplier that's more local to you.
If the idea of having to chop up a lot of tangle-prone biomass is daunting, you could also consider planting winter rye. It doesn't add nitrogen like the vetch or peas, but it does trap the nitrogen you'll be adding in the manure, preventing it from being lost. Rye can take a couple of passes with the tiller to kill completely, but if you hit it before it puts on too much growth, it doesn't get tangled. Beware that rye must be killed at least two weeks before planting seeds in the soil, because it gives off chemicals that prevent seed germination -- transplants aren't affected.
Lastly, are you composting every bit that you can? Everything that leaves your garden takes some nutrients with it. Vegetable waste from your kitchen (rinds, peels, the forgotten lettuce that rotted in the back of the fridge, etc), along with garden debris (vines, leaves, etc) should be composted and returned to your soil so you don't have to purchase so many outside amendments. Don't put autumn leaves in bags on the curb -- this is valuable carbon you can mix with kitchen scraps in the compost pile and return to the soil.