add {} braces when checking for cookies is null or not. when you load you page at first the cookies are not set that's why you are gettin that exception.

protected void Page_Load(object sender, EventArgs e)
{
if (!IsPostBack)

if (!(Request.Cookies["FirstName"] == null) && !(Request.Cookies["LastName"] == null))
{
TextBox1.Text = Request.Cookies["FirstName"].Value;
TextBox2.Text = Request.Cookies["LastName"].Value;
}
}