The Design and Use guideline that was referenced to does allow for the use of fences for dog runs:
10. Fences. To retain the natural beauty of the community and allow wildlife movement across and
through Lots, fences need to be limited to dog runs and not serve as lot boundaries. These pet
fences should be constructed of transparent and not privacy screening materials.
Since there is not size restriction, you should be good. Just make it from a transparent material, buy which they must mean something like a picket fence that has an appropriate spacing for your dog.