So you don't like de default Date Picker icon? The good news is that there a very simply way to change it.
First of all, you need to have a nice icon. I suggest this website where you can find a lot of beautiful and free icons. Now that you have the icon file you need to upload it to your system. If you don't want to upload to the filesystem, you may follow this path "Shared Components>Images>Create Image" and upload it to APEX static files.
Now to set your icon as Date Picker default you need to update your application Theme. Go to the Themes option on Shared Components and edit the default theme. Then, click "Calendar Icon Details" and enter the path to the uploaded image file.