Here is the correct code:
var columnsNotHidden = new Array();
var columns = $("#grid1").data("kendoGrid").columns;
if (columns.length > 0) {
for (var i = 0; i < columns.length; i++) {
var col = columns[i];
if (col.field != undefined) {
if (col.hidden != true) {
columnsNotHidden.push(col.field);
}
}
}
}