Hello, are you able to take a close up photograph?
What is the distribution of the patches....ankle, shin, front or back of leg etc?
Are both legs affected?
What is the size of the patches?
Any itch, heat or pain?
The first thing to establish is whether this is a contact reaction to grasses, insect bites or other plant material (some plant sap cause a severe photosensitive reaction). It can even be a reaction to woolen walking socks.
However a sudden onset problem with prominent small blood vessels may be a cutaneous vasculitis. This is inflammation of the blood vessels which explains the physical appearance of red vessels.
Another possibility is capillaritis which is inflammation just of the capillaries. This may change to a brown color and fade with time. It is very common after exercise.
As we do not know if this is a vasculitis, then it would be a good idea to see a doctor for a physical examination and some blood vessels. As he feels otherwise well then this could wait until after the weekend to see your own family doctor.