I'm cleaning out my barn. It's old cow manure that's been in there for 20 years. I put a bunch of it on the garden, which has clay soil. I'm growing tomatoes, peppers and onions.
Will this hurt my vegetable garden?
Unless harmful elements fell into your manure during those 20 years without your knowledge, it certainly shouldn't hurt anything. It might not be as potent as properly matured and composted manure, that's all.
Concerning your clay soil : don't work in your garden if it rained in the last 2 days to avoid compacting the soil.
Sounds like perfect stuff. You are going into winter, yes? If you are, just put it on top of the beds thickly. This will help keep the weed seeds already in the soil from germinating as well. In the spring, when your soil has dried, double dig your vegetable beds 3' in width throwing the clay soil on top of the manure. Micro and macro organisms have been coming up out of the soil profile to eat the decomposed organic matter and they go back down into the soil to poop out their dinners, mixing it into the soil for you.
Because you have clay you really need plant beds built up to increase the drainage and help warm the soil for early planting. This doesn't mean using wood or bricks or anything for sides. Double digging a good foot down into that plant bed will quickly 'fluff' up your soil. Don't worry about mixing or doing anything other than turning over your soil using a shovel. Never use a rototiller for clay soils. Clay is flat tiny pieces of rock and the surface of these little rocks being flat has a huge electromagnetic charge causing the rocks to adhere to each other. That is why they use clay in concrete, along with gravel, lime, gypsum, water and rotation.
Dig a trench 6"X6" along all the sides of these beds, throwing the soil up onto the bed. Even the soil out with a rake so it is the same height, get a piece of plywood, throw it on top of your bed and jump up and down on it. Move the board and do it again until you've done the entire length. You are now ready to plant. If you do seed you can broadcast instead of making straight lines and by raking the sides UP, pulling the soil along the sloped sides up and flipping loose soil on top of the bed to lightly cover tiny seeds like lettuce or I push the large seeds down to their best germinating depth then flipping soil up from the sides.
Leave the walkways alone. They should be inhospitable to any growth, firmly packed. Hope this makes sense. Drives me nuts to see gardens started on flat, cold soils. When you get done with each bed you can look back at your garden and be quite proud. I do this will any type of soil.
Do not confuse this decomposed manure with soil or fertilizer. Its job is to add organic matter to the top soil. You can keep adding this same manure to the top all year long. Try to do a 'green crop' or 'cover crop' the next winter on your beautiful beds to add more organic matter and out compete weeds to your beds. Can't over do adding organic matter to your soil.
Get a soil test before and the next year to see how much your soil has changed. If you need a more alkaline soil or a more acid soil you'll be able to know which beds are best for potatoes for an example because they have a 5.5 pH soil. Other beds could have a 6.5-7.0, or whatever pH your specific crop needs.
Great find and I am glad you aren't wasting this manure. It is gold. You should find out the animal husbandry of the herd owners. Were any of the cattle on antibiotics? Did they have mad cow disease? I doubt that but you see my point. Lots of weed seeds in the manure but big deal.
In addition to what has already been stated, I would be careful not to rely on just cow manure. It would be beneficial to mix in other nutrients to the soil depending on the vegetables you are growing. For example, I mix horse manure with chicken manure to my vegetable garden. Then during the growing and harvesting season, I add other organic fertilizers as well.