DO YOUR OWN TEST - AZIMUTH
Determining the date of the winter solstice by observation of the azimuth of the sun at sunrise or sunset does not require either the determination of the direction south nor the use of a clock to determine the time.
Rather, it only requires an observation at, or near, sunrise (sunset) of the position of the sun on the horizon, noting when it reaches it's most southerly position and starts returning north.
This might be done by observing a shadow, similar to the method described under the Elevation method.
However, it is more usually done by placing your eye at a fixed position and noting the position of the rising sun relative to land marks, such as a building, telephone pole or tree, on a distant horizon - prior to the sun rising to the extent that it can no longer be viewed by the naked eye. Alternatively, if you have a steeply sloping mountain or similar large item visible in the distance, you can use it's shadow as a marker by positioning yourself so that you can just barely see the trailing edge of the sun as it rises in its angular path. So doing will allow you a longer period for the observation than observing the sun on a flat horizon. This discussion assumes that you are not so lucky.
Most ancient sites had a single point on the horizon fixed by the placement of two vertical stone edges so aligned that when you positioned your eye such that they appear to nearly touch you could see only a slit of the sun as it set, or rose, when in that position. Thus, they could accurately tell when the leading or trailing edge was just visible.
(Viewing the setting sun is easier since you know where to look, whereas seeing the first portion of a rising sun requires that you knew where, and at what time, it rose yesterday.)
Of course, the stones at ancient sites were firmly set after they already knew where to set them. To determine where to set them requires that they be able to be repositioned on successive days until the least, or greatest, azimuth angle is observed.
One way to do this is to simply take a picture of the rising or setting sun on successive days, and then pick out the one that shows the least, or greatest, azimuth when viewed from the fixed point where the picture was taken.
Note: You will need a dark filter for your camera if you plan to take pictures of the full sun, or if your horizon is not distant (less atmosphere to momentarily filter the light for you).
Another simple method is to use a camera tripod with a head that swivels in the horizontal direction, and that can be locked in place after each observation. Instead of a camera, install either a compass or a flat surface on which two raised objects with straight vertical sides are placed some distance apart. Then simply align the objects each day so that you can just barely view the leading or trailing edge of the sun as it rises or sets. The winter solstice will occur on the day on which the flat surface, or objects on the surface, have been rotated the maximum degree towards a southerly direction.
Note that the required accuracy of your setting is set by the fact that the daily angular increase in the azimuth just prior to the winter solstice is only approximately 1/2 arc minute. By comparison, the angle that the sun's diameter subtends with your eye is approximately 30 arc minutes. Thus, your accuracy must be approximately 1/60th of the diameter of the sun. Accordingly, you should set your objects so that you only observe that much of the leading or trailing edge.
These observations will not be made at the exact same time everyday since the time of sunset changes slightly each day. Since it is difficult to look at the sun directly in full daylight, the best approach is probably to make the observation just as the sun has sunk until the lower edge has reached the horizon (when you can see the full diameter, and to then observe either the leading or trailing horizontal edge. It will take about two minutes for the sun to fully set so you will need to be ready in advance to rather quickly make your observation while the full diameter of the sun is visible. Select TIME AVAILABLE under Azimuth to see how much time is available.
It may be noted that such an observation will not be of the sun actually sinking since the earth's atmosphere bends the light downward, causing you to view the setting sun after it has already set. (Of course, if your horizon is not distant then very little bending will have occurred, and you may need to filter the light to protect your eyes.)
In making your observations you should note that the sun does not rise vertically, except at the equator, but rises at an angle which is related to your latitude. As an example, it rises at an angle of about 45 degrees at San Francisco, California. Accordingly, instead of using a verticle object for your shadow of the sun, you should use a shadowing object which has the angle which is appropriate for your latitude. For instance, the "heel stone" at Stoneheng has such an angle. Select Marking/Spacing for a detailed discussion of this problem.
Once you have determined the position of the setting sun on the solstice you might want to establish a more permanent record of that position by noting exactly where it was on the horizon, by setting up a pair of your own markers aligned with that position - or perhaps taking pictures on several days before and after the solstice and selecting the correct one as a reminder when you are looking for it next year.
While you are at it, if your horizon is several miles away, you may also see a special solar phenomena called the Blue Flash. As the sun sets the atmosphere bends different wave lengths differently, with the last wave lengths visible being the higher energy shorter wave length ultra-violet, blues and greens. While you can not see the ultra-violet you can see a very brief (one second) blue-green flash just as the sun completely disappears over the horizon. Click here to see a NASA photograph of this phenomena.