For a number of reasons, Saudi is not a pedestrian friendly place. The most popular reason would be the brutal heat, which really does preclude walking anywhere in the daytime for a good five months out of the year. But another reason is simply a matter of urban planning - there is no consistent network of sidewalks in this region, so on any given road, you may be walking on sidewalk for a part of it, then the dirt part of a construction zone, then the road itself while you walk around construction barriers, and then back onto a sidewalk. Many of the smaller streets do not have sidewalks at all. Also with the exception of a few parks, a couple of nice streets, or walking around the souks, the lack of control in organizing the growth of the city has led to a disparate (read in: ugly) looking landscape that is not worth exploring on foot.
OK so for all the above reasons, there are pretty much no pedestrians walking around the city, and especially not the abaya-wearing delicate flowers known as women. But from time to time, you just can't avoid walking. Given all the information above though, any time a taxi driver sees a woman walking, they think "oh! she needs a ride. Why isn't she looking at me? I'm gonna let her know I'm here." *HONK* Then they slow down to see if you are looking, which causes all the cars behind the taxi to honk the taxi. *HONK* *HONK *HONK* You must make eye contact and shake your head or wave them away before they move on. Now this is the important part: repeat this fifty times, because THAT my friends, is what taking a walk in Riyadh is like!