problem with <select> and :after with CSS in WebKit

To my experience it simply does not work, unless you are willing to wrap your <select> in some wrapper. But what you can do instead is to use background image SVG. E.g.

    .archive .options select.opt {
    -moz-appearance: none;
    -webkit-appearance: none;
    padding-right: 1.25EM;
    appearance: none;
    position: relative;
    background-color: transparent;
    background-image: url("data:image/svg+xml;charset=utf8,%3Csvg xmlns='http://www.w3.org/2000/svg' version='1.1' height='10px' width='15px'%3E%3Ctext x='0' y='10' fill='gray'%3E%E2%96%BE%3C/text%3E%3C/svg%3E");
    background-repeat: no-repeat;
    background-size: 1.5EM 1EM;
    background-position: right center;
    background-clip: border-box;
    -moz-background-clip: border-box;
    -webkit-background-clip: border-box;
}

    .archive .options select.opt::-ms-expand {
        display: none;
    }

Just be careful with proper URL-encoding because of IE. You must use charset=utf8 (not just utf8), don't use double-quotes (") to delimit SVG attribute values, use apostrophes (') instead to simplify your life. URL-encode s (%3E). In case you havee to print any non-ASCII characters you have to obtain their UTF-8 representation (e.g. BabelMap can help you with that) and then provide that representation in URL-encoded form - e.g. for ▾ (U+25BE BLACK DOWN-POINTING SMALL TRIANGLE) UTF-8 representation is \xE2\x96\xBE which is %E2%96%BE when URL-encoded.

I was looking for the same thing since the background of my select is the same as the arrow color. As previously mentioned, it is impossible yet to add anything using :before or :after on a select element. My solution was to create a wrapper element on which I added the following :before code.

.select-wrapper {
    position: relative;
}

.select-wrapper:before {
    content: '\f0d7';
    font-family: FontAwesome;
    color: #fff;
    display: inline-block;
    position: absolute;
    right: 20px;
    top: 15px;
    pointer-events: none;
}

And this my select

select {
    box-sizing: border-box;
    -webkit-box-sizing: border-box;
    -moz-box-sizing: border-box;
    width: 100%;
    padding: 10px 20px;
    background: #000;
    color: #fff;
    border: none;
    -webkit-appearance: none;
    -moz-appearance: none;
    appearance: none;
}

select::-ms-expand {
    display: none;
}

I have used FontAwesome.io for my new arrow, but you can use whatever else you want. Obviously this is not a perfect solution, but depending on your needs it might be enough.

I haven't checked this extensively, but I'm under the impression that this isn't (yet?) possible, due to the way in which select elements are generated by the OS on which the browser runs, rather than the browser itself.