I have been researching the Churchill family for 30+ years. In my database of 67000 files, I have 8 Moulton individuals that had connections by marriage to Churchills. Most are from Ontario ( Canada West ) and a few from New York. They are:
FA Moulton, Herman Moulton, Ivy Moulton, JH Moulton, Joseph Moulton, Oliver Moulton, William H Moulton and William John Moulton. Some of these may ring a bell. I do not have detailed information on them, only on their Churchill connection.
As Sir Winston Churchill is actually a Spencer and not a Churchill ( read comments a few questions down for an explanation ) there is not a proven connection to North American Churchills. You might have to search for a connect through his wife's or mother's family.