When a goat is rubbing fur off (to the skin, not just normal shedding itching), the first thing to suspect is mites or lice. Take a close look and go through their fur. Mites or lice is especially probable because they tend infest animals heavier during colder months. Which is why shaving the goats down during warm weather is a great preventive measure, for that time of year, as you can imagine, it is a bit too cold for that method.
The only way to confirm mites is a skin scraping under a microscope. But you can physically see lice, especially if you use a nit comb to help you find them. Don't worry, goat lice will not infest humans, dogs, etc. they are rather species specific.
I'd recommend treating the two with ivermectin pour on. It is dribbled down the base of the spine, making sure to get it to the SKIN with the applicator (I use a needleless syringe to apply it) by parting the fur. If it gets just on their fur and not down to the skin, it won't do any good Repeat the treatment in 10-14 days, then again, in another 10-14 days. This is to kill the buggies at all stages of the lifecycle. It is applied to goats topically at a rate of 1cc per 20lbs of goat, and it is hard to overdose, so don't worry if you overestimate a little. If you underdose, it won't work as well, and your goats will not get relief.
Also, it would be a great idea to remove all their bedding. When you add new bedding, either dust it down with diatomaceous earth of PYthon dust. One is a chemical, one isn't and kills buggies through mechanical means. It will be extra insurance to make sure they are cleared of whatever is infesting them.