Being as it was summer and a full moon out, I think you might have come across one of these that had probably escaped from a nearby ranch.
In the darkness these would appear pretty much as you described and as for the eyes glowing amber the moon was full so probably enough reflection to create this appearance.
Below are a couple of ranches in your general area showing that these cattle are around there.
"Here in the So. Oregon mountains near Crater Lake,** they fair well during winters with knee deep snow and, upon occasion, below zero temperatures and cold blowing winds. The varied terrain and trees give them all the protection they need, although many times they will lie or stand in the open with a coating of snow on their backs. The same goes for the summers when 100 degree days are common. The cattle find a spot of shade in a grove of trees or stand in a creek or pond during the heat of the day, then graze at night."
Bold is my emphasis
" They are bright and responsive, with each animal knowing its name and the herd coming to a whistle. "
One of you wouldn't have been whistling a tune while walking on the beach would you? ;-)
You might check around there and see if there is a ranch which had this breed around the time you had this incident.