Styling an input type=number

Is it possible to apply a style in the inner "up arrow" and "down arrow" of a <input type="number"> in CSS? I would like to change the background of the up arrow to blue and the down arrow to red. Any ideas?

UPDATE 17/03/2017

Original solution won't work anymore. The spinners are part of shadow dom. For now just to hide in chrome use:

input[type=number]::-webkit-inner-spin-button {
  -webkit-appearance: none;
}

<input type="number" />

or to always show:

input[type=number]::-webkit-inner-spin-button {
  opacity: 1;
}

<input type="number" />

You can try the following but keep in mind that works only for Chrome:

input[type=number]::-webkit-inner-spin-button { 
    -webkit-appearance: none;
    cursor:pointer;
    display:block;
    width:8px;
    color: #333;
    text-align:center;
    position:relative;
}

input[type=number]::-webkit-inner-spin-button:before,
input[type=number]::-webkit-inner-spin-button:after {
    content: "^";
    position:absolute;
    right: 0;
}

input[type=number]::-webkit-inner-spin-button:before {
    top:0px;
}

input[type=number]::-webkit-inner-spin-button:after {
    bottom:0px;
    -webkit-transform: rotate(180deg);
}

<input type="number" />

For Mozilla

input[type=number] { 
    -moz-appearance: textfield;
    appearance: textfield;
    margin: 0; 
}

For Chrome

input[type=number]::-webkit-inner-spin-button, 
input[type=number]::-webkit-outer-spin-button { 
      -webkit-appearance: none; 
      margin: 0; 
}