I believe below solution gets what you want. Just few lines of CSS (explanation below snippet)
Warning
Styling <select> and <option> elements is not supported across all browsers, because they are rendered by OS, not browser. There are external libraries that create select-like elements composed from HTML elements that can be styled. Below solution is not 100% safe.
Snippet
#select-id {
  color: red;
}
#select-id option:not(:checked) {
  color: initial;
}
<select id="select-id">
  <option value="" selected="">Pick a Country</option>
  <option value="">India</option>
  <option value="">Sri Lanka</option>
  <option value="">Sweden</option>
</select>
 
 
Explanation
#select-id {
  color: red;
}
Makes select and all options have color: red.
#select-id option:not(:checked) {
  color: initial;
}
Makes not-selected options have initial color, which is black.