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Cattle are lovely creatures most of the time. They can be very serene, curious, and playful! But you have to remember that fully grown they are also very big, well over 1/2 ton in weight. You also have to remember that they hang out together in a herd, and therefore you are dealing not with individual animals, but a herd mentality. They get frightened very easily. If one animal takes fright because your coat unexpectedly flaps in the wind, the whole herd are likely to presume the worst and leg it out of there as fast as they can. That's pretty much a stampede, and that's where people and animals can get hurt. There are two breeds of cattle that stampede in an instant, Limousin and Blonde D'Aquitane. They're dark red or black in colour, and pretty muscular. Avoid them.
There's also the danger of a moody bull, and if you're unfortunate enough to encounter one of those he will outrun you surprisingly fast. He can be hidden among the cows in a large herd, especially in the spring time, so you might not see him at first glance. Cows with newborn calves can also be agressive, and act similarly to a bull.
Having said all that, under the right circumstances, it's nice to say hello to a cow. They're very grounded and serene when they're relaxed, and they'll share that with you. Find a farmer who'll accompany you, or try an open/holiday farm where the cows are used to being petted by strangers, but don't venture unannounced into a field of unknown cattle. Or maybe just admire them from behind the safety of a gate, or a well fenced hedge! Or go to the ploughing match in October, or a county fair. The cattle on show there are very quiet, and the farmer will be standing beside them to introduce you.