If cows could photosynthesize, how much less food would they need?
In a way, they already do. A field of grass sits there all day soaking up energy from the sun and storing it chemically. A grazing animal can then come along and absorb weeks of accumulated energy in a matter of minutes.
A Jersey cow presents in the neighborhood of nearly two square meters of usable space to the sun if it stands right. (Cows would have to be trained to stand optimally, but we might not have too far to go; research suggests they already align themselves north-south.
Chlorophyll photosynthesis extracts 3%-6% of the total energy from sunlight. If we figure on any given day the cow gets the equivalent of about six hours of peak sunlight, it works out to less than two million joules of usable energy each day.
Is that a lot? Well, a 450-kilogram cow just wandering around in a field might eat about 10 kilograms of dry matter a day, extracting on the order of 50 million joules of metabolic energy. So photosynthesis could only make up about 4% of the required intake—saving only a few handfuls of grain.
If we could equip cows with solar panels, which can be several times more energy-efficient than photosynthesis, we could improve that number—but not by much.
The basic problem facing cows is the same one facing solar cars—they're too small. If you saw the world's cattle population in silhouette, they'd have an overall cross-sectional area of about two thousand square kilometers. This means that if they were migrating through the air over Rhode Island (biology is not my strong suit), they'd blot out the sun over barely half the state. They'd only catch enough sunlight to produce a daily average of about 40 gigawatts of power (two megayodas).
By contrast, about 3% of the world's surface area is cultivated, which means that (given rough estimates of geographic distribution of farmland) our crops easily intercept over a thousand times more sunlight than our cattle—which is why grazing is a good strategy.
I'd like to conclude with this quote, which I found in the Cedara Agricultural Development Institute's Applied Ruminant Nutrition for Dairy Cows:
Cows on a typical dairy ration can produce 80 to 100 litres of saliva per day.
This has nothing to do with photosynthesis, but I wanted to share anyway.