I know that barn kittens usually stay in the barn, but this could be a matter of life or death. I think you need to have the kittens and mother cat in your room, where you can weigh them, keep their bed warm, and supplement their feedings, if necessary. You will know if one is in distress if you keep them near you.
Doodle gave you the best possible advice. A life is a life, whether it's a pet or a barn cat. I'm sure you'd agree. Those babies need extra warmth and extra attention, perhaps a vet's attention. It would be wise to get a heating pad made especially for kittens and puppies, one that doesn't get too hot. However, if that's not possible, follow these directions:
http://en.allexperts.com/q/Cats-1606/ne ... mother.htm
Kittens must remain warm at all times. Get a cardboard box and some towels and line the box with the towels. Put a heating pad on one side of the card board box so that if the kittens get to hot they can move over to the opposite side of the box where the heating pad isn't located.
Kittens must be fed every three to four hours or they will die. You cannot give them regular milk as this is useless it will do nothing but cause diarrhea and soon death. The food you must feed the kitten should be a kitten milk. Take a trip to a local Petsmart and purchase KMR Kitten Milk you will need a lot of these so get as many as you're able to purchase. You will need to feed them through a eyedropper, syringe, nursing bottle, or stomach tube. A small syringe or eyedropper is easiest for inexperience hands. If a nursing bottle is used the holes in the nipple should be enlarged if the formula does not drip slowly from the nipple when the full bottle is inverted (turned upside down)
Make sure the heating pad is on low and is covered. A heating pad especially for cats is better, because you can keep the temperature lower. However, you need to take action immediately!
Although that article is about abandoned kittens, these kittens are cold, and the two issues covered are the most important. Keep them warm, fed, and, of course, call the vet. If you use goat's milk, mix it 50/50 with sterile water, and use a kitten nursing bottle. Make sure the milk is at room temperature and kept refrigerated between feedings. If you don't have a nursing bottle, a dropper will do. Whether or not this is necessary will depend on the kitten's weight.
When preparing formula, make up only enough for a forty-eight-hour period and divide it into individual feeding portions. These portions can be stored in the refrigerator. Before feeding, warm the formula to about 100° While warming the formula, sterilize the feeding utensils in boiling water for fifteen minutes to destroy harmful bacteria or viruses. All handlers should wash their hands before feeding or handling the kittens.
Do your barn cats get their vaccinations and veterinary care? It's so important. Please let us know how they are doing.