On the Cape Wrath Trail I came across a Highland cow ambling back and forth along a path kicking up a hell of a racket. Before I Ieft I had read that a few weeks previously a hiker had been injured up there by one so I was very wary. I climbed off the trail and went round it. Back on the trail I came across a dead calf and figured that was all the fuss was about; the cow was bereft.
You need to have an escape route planned to give you a few seconds start if something is happening. I saw a sign once -The bull runs from gate to gate in eight seconds can you do it in seven?
In the US a hiker told me that he had been treed by a Black bear which climbed up after him. He spent about two hours poking it in the face with a sharp branch he had broken off. He won in the end.
Martin I reckon when your horse and dog seek eye contact they want something and are seeking assurance that you are going to give it to them.They are establishing the signal with you.
I am no expert by the way though I was raised on small holding with lots of animals.Bullocks are young and daft and unpredictable. In line with other stock cow herds will have dominant females who make decisions which way to go, when to lie down etc
I too have had the stock herd at a stile experience and thought " I'm a country boy I can cope with this," so I gave the nearest a slap on the backside and it turned its head around and had the biggest broad bull head I had seen for quite a while, having made my point I was over the stile faster than Usain Bolt.
Good advice above. With all animals I recall avoiding direct eye contact is recommended especially with big stuff you cannot fight. Pack animals certainly see direct eye contact as a threat.The eyes have it as a signal area.