And Yes, we're trying to use OOTB control, which is pxDateTime.
I've checked the image of control in HTML tab, there's a image configured: images/pz-date-time-active.svg; and I can see the image well. But it seems the image specified here isn't used in the user portal.
And the generated HTML code of user portal as below:
<img src="name='CalendarImg-72fd9b28'" class="inactvIcon" data-ctl="["DatePicker"]" style="cursor:pointer;" tabindex="0" role="button" alt="Choose from calendar">