Short answer: yes, dogs can get cold. While arctic breeds (huskies, malamutes) are wearing the equivalent of a high-end layering system, other breeds are wearing a t-shirt. Very young or very old dogs will feel the cold more than healthy adults, and very small dogs tend to get colder more quickly than larger ones.
Tip: do some short test adventures outside in early winter with your dog. You can get an idea of how comfortable they are outside in different temperatures, and what winter coats or winter boots for dogs might be beneficial for them.