No it can't. A fence 'counts' as being a block and a half high, so players and mobs are unable to jump over it - though a spider can climb it as Spiders treat all vertical surfaces as if they were ladders.#
Sometimes a cow can glitch out of an enclosure, not much you can do about it.
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Didn't you mean a Fence Gate that opens? or a Fence? Well... To make a fence, you ________ | | | | | | |________|
You can't tame a cow on Minecraft, however, you can get it to follow you by holding wheat. With two wheat, you can mate two cows by right-clicking on each cow. A baby cow should appear. This is called "cow farming."
Press the spacebar
Right click a cow with a bucket.
They don't eat... yet.