.Textinput .Textinput-Clear {
    right: 0;

    display: none;
    visibility: hidden;

    cursor: pointer;
}

.Textinput-Clear.Textinput-Clear_visible {
    display: block;
    visibility: visible;
}

.Textinput_disabled .Textinput-Clear_visible {
    z-index: 0; /* Понижаем под Control и Box */

    cursor: default;
}