Unfortunately, American goats are bred for high grain input and it is hard to find one who can maintain their weight and produce milk on just forage; however, I believe it is doable. It would never work with the Registered Saanens I have, they are high production and need high input. I have one Nubian doe, two years old, who gets a little grain, but stays fat and produces 2 1/2 quarts of delicious, high butterfat milk per day. Not a high producer by any means, but
sustainable on very little, very hardy and healthy too. Her legs and fetlocks are straight and she wears down her hooves evenly, so I only trim her feet about once a year, and honestly, she doesn't need it then. By little grain, I mean about a cup twice a day, of sunflower seeds and oats with a dash of dried molasses on top. She also gets free choice goat mineral. If I could grow enough butternut or pumpkin, have enough dried tree leaves and acorns for her year round, I think she would pass muster. She's slick and shiny, and in good flesh.
I've tried making "hay" for goats, out of things other than grass...such as lespedeza, dried tree leaves such as black or
honey locust, maple and mulberry. The lespedeza, locust and mulberry are all high in protein. Past winter, I ran short on pasture and hay due to having a cow/calf I normally don't have on my small farm. I cut branches from the bamboo, which they loved. Even the cow would come running when she saw me walking down there with the pruning shears in hand. It is about 15 percent protein. High humidity here, in temperate rain forest, means even the best dried and cured hay won't keep long. They also love a handful of acorns all winter, in place of grain ration. It gives them good essential fatty acids, starch and protein. Makes the milk taste good too, with higher than normal butterfat. I grew butternuts and pumpkin for them last year, and all winter, I split and cut up one per day for them until I ran out. This spring I'll plant a bigger patch as now I know how much they love it. Pumpkin or squash seed kill tapeworm too, so it helps keep them wormed.
It should be pretty easy to grow a patch of sunflowers, and dry them for winter forage. Sunflower can get buggy if stored too long, so be aware. One or two goats would certainly be easier to feed than a herd. When green, they love the whole head (try it, you'll like it too). The leaves make excellent dried fodder. So can corn leaves.
Summers are easier, and even spring, when the wild roses put on new growth, and the honeysuckle grows rampant. Blackberry briers are a high nutrient, high mineral plant for goats and they will clean out a patch. Goats love both of those and need them to have truly good health, but sometimes cut their udders on the thorns. I planted wild roses along the long driveway coming in so it would grow through on one side into the pasture, and they would trim it. They certainly do. I planted Forage Feast Chicory on the back hillside, along with lespedeza and a mix of dandelion, trefoil, clovers, various grasses for summer. I have to rotate them off quickly or they would graze the chicory to extinction. It is another high nutrient crop, and makes them gain weight quickly and produce more milk with higher butterfat. That particular variety was developed in New Zealand to have greater nutrient density and higher digestibility. The goats and cow search it out. I haven't noticed that it flavors the milk in a bad way, but they are getting a good mix.
Root crops are a good source of calories, but turnip roots, fed in much quantity can give them bloat and also give the milk a bad taste.
It's very important to NOT feed young goats grain. Make them work for a living, get out there and eat and develop their rumen. If they get grain or even too much of mama's milk, they won't be hungry and will lie around and sleep all day and the rumen is never developed as well as it should be. Yes, give them their milk, but let them go part of a day without it so they will eat forage. If the rumen is not developed when young, it never will be to full capacity and then, no matter how great the forage is, they can't eat enough to sustain themselves. Goats don't do well with grain anyway, their stomachs aren't made for it. However, an animal giving two gallons of milk a day would starve if she had to forage for enough to provide the nutrients to make that. Keep in mind too, that green forage contains a lot of
water, and they need something starchy and something dried to get more calories.
The more moisture in the forage, the more dried matter they need to counter balance so they don't get bloat. Just like cows. As they get used to it, they will bloat less, but even then, they need the calories.