If you want to build a cottage and have a location that features exposed bedrock, consider yourself fortunate. This will save you the trouble of excavating and will supply you with an extremely stable basis for your construction. When you have bedrock available, the foundation of the cottage doesn't need to do much more than provide a flat surface on which to build, because the bedrock is providing all the necessary stability.
A frost wall will provide the most protection against cold because it will protect the floor of the cottage from winds and drafts. To build a frost wall directly on rock, you need to create a flat basis for the wall. You can do this by constructing concrete forms and pouring a footing directly onto the rock. The footing only needs to be high enough so that the whole floor is flat. For example, if the difference in elevation over the span of your planned foundation is 10 inches, you could pour a footing that was 12 inches high at the rock's low point and only 2 inches high at the high point. You can then build a frost wall of concrete blocks on top of the footing.
Concrete posts lift the floor of the cottage off the ground and provide a solid connection between the bottom of the cottage and the rock beneath it. A small cottage that is 10 feet square or less doesn't need more than four concrete posts, one located at each corner of the cottage. To build the posts, you can use commercial Sonotubes, cardboard cylinders into which you pour concrete, or you can build your own forms out of scrap wood. Either way, take care to make the concrete posts perfectly vertical.
In the days before readily available concrete and other manufactured products, many cottages, barns and even complete houses were constructed on nothing more than flat rocks. If you stack the rocks solidly, a building can stand on them for decades with no problem. When using this method, take your time to find exactly the right rocks and to stack them so no movement is apparent. This can involve a lot of moving around and rearranging of rocks, but the result can be an interesting look as well as a solid foundation.
Wood is not as durable a foundation material as concrete or rock, but it is easier to use and often less expensive. If you are building a cottage on bare rock in the desert or in another dry environment, wood will perform better than in a wet place, because the main threat to a wood foundation is wet and rot. Place vertical wood posts at the corners of the planned cottage directly on the rock face, then trim the columns so that their top faces are level with each other. Strengthen the columns by connecting them with cross braces.