The AJAX is done solely by Javascript in the browser. It must have a proper URL to fetch its content from. For example, if you have a snippet in a resource with the alias "test", then the AJAX URL would be domain.com/test.html Other AJAX methods will have different ways of dealing with variables, but they all work on the same principle.
If you are using JQuery for your AJAX, just pass the variables in the second paramter of the load() function:
$("#objectID").load("test.php", { 'choices[]': ["Jon", "Susan"] } );
http://api.jquery.com/load/
Using JQuery ajax() function:
$.ajax({
type: "POST",
url: "some.php",
data: { name: "John", location: "Boston" }
}).done(function( msg ) {
alert( "Data Saved: " + msg );
});
http://api.jquery.com/jQuery.ajax/
So you would get your color value from the color picker, save it as a Javascript variable, then use that variable as the value of the variable:
var color = the results of the color picker; perhaps the value of a field?
("#objectID").load("test.php", { 'color[]': [color] } );