The short answer. YES!!!!
These bratty, and seemingly fragile creatures are much hardier than you may think. Our chickens have lasted through many cold days and night, CHOOSING to spend time outside along the way. And while the goats are reasonably new to us, they have already proved their superiority compared to us humans when it comes to comfort outside in the winter! That said, there are some things you want to make sure you do for your animals to help them withstand particularly cold days or nights. Everyone has different practices, but this has worked splendid for us!
1) It is important NOT to baby your animals. Now, if you have a heated barn that will always be heated go ahead, bring out the jackets and the heat lights and everything. Those spoiled babies are gonna be thrilled! BUT, if you do not have those things or you do not plan to use them 24/7 then its best to avoid using them at all 99% of the time. If allowed to experience the changing season in a draft free barn with the other members of the herd, their coats will change to adapt to these conditions. If you use a heater all through november and december, they wont adapt and will be left severely underdressed for the rest of the winter!
2) Especially with goats, it is crucial that they eat, eat, eat during the coldest times of the year. Free access to hay is 100% necessary!!! There are many awesome articles online to back up the science but as ruminants, much of their digestion works to keep them warm!
3) Make sure your goats and chickens are not forced to sleep on the ground or floor. This means a perch in the coop or raised beds in the barn, we made some very simple raised beds out of plywood, 2x4s, and stumps! They will thank you!
4) And lastly, providing them with warm water a very minimum of two times a day will not only feel like a treat to them, but is very helpful in keeping those cute little bodies warm and happy! If you have a water heater already (lucky!!), you wont have to worry about this. But if not make sure you are making that trip, even if the water hasnt frozen!