[bes]

<input type="button" value="Следующий">Текст:
<input id="output" type="text">
<script>
var arr = ['зима', 'весна', 'лето', 'осень'],
	iterator = arr.keys();
document.querySelector("input").addEventListener("click", function () {
	var next = iterator.next().value;
	if ( !next) {
		iterator = arr.keys();
		next = iterator.next().value;
	}
	this.nextElementSibling.value = arr[next];
});
</script>