In the Laura Ingalls Wilder book The Long Winter, Laura's father says that you can predict the severity of a winter by observing the thickness of muskrat nests in the summer. Muskrats, he says, will build thicker nests during the summer if the following winter is going to be relatively colder, and vice versa with thinner nests and relatively warmer winters. Has this folk wisdom been investigated? Is it true? And if so, where can I get my own muskrat colony?
I can't find anything on Google Scholar or Web of Science indicating that anyone has published anything about muskrats and weather prediction, other than this:
Man's natural craving for advance knowledge of coming weather extends thousands of years back of any attempts at scientific weather forecasting. Realizing that he has not the necessary foresight himself, he has imagined animals to be endowed with some peculiar sense which enables them to know, weeks or months ahead, what the weather will be. Thus a large group of animal weather proverbs has come into existence. Millions of people believe that the thickness of fur on a muskrat, or the number of nuts stored by a squirrel, or a supposedly early migration of certain birds, indicates a severe winter. Yet it is certain that animals have no such foresight.
from: Robert DeC. Ward. 1926. The Present Status of Long-Range Weather Forecasting
Proceedings of the American Philosophical Society,Vol. 65, No. 1, pp. 1-14
He provides no evidence to show that they don't, he is just certain. Note that the version you mention has to do with the thickness of the wall of the house, while the version Ward mentions has to do with the thicknesss of their fur. The fur hypothesis would be easier to test, if you were a muskrat hunter. I am frankly doubtful whether he or anyone else has done the work that would be needed to convincingly either story. You would have to measure the wall thickness of bunches of muskrat houses (or the pelt of many muskrats) in the summer. You would have to do this every year for quite a few years in order to make a convincing analysis of the relationship between wall thickness and hardness of winter. You would probably also want to measure various features of the microclimate, the muskrats behavior and physiology, and the local ecology, in order to get some sense of what the mechanism was. You probably would want to measure the pelts and the houses, just to make sure you were measuring the right thing. This is one limitation to testing folk-wisdom. There are often several versions, and it is hard to know if you are testing the right one unless you test all of them, and then you increase your chances of finding a strong correlation just by chance. My best guess is that there is some, but not a lot of, truth to either version of the story. Certainly they could pick up on whatever cues are available that the winter is going to be hard. But like most weather prediction, they probably aren't very accurate, at least not months in advance.