Hello Huzefa,

More likely, in WebInput the arrow is handled by DateTimeEditor. 
You will need additional style if you want to configure its style. Add "Webdings" font should resolve the issue. Our arrow icon use "text" as default which is Webdings.

<DropDownStyle>
      <Active BaseStyle="Over" Font-Names="Webdings">
      </Active>
      <Over BackColor="#E9E5D9" BaseStyle="Normal" Font-Names="Webdings">
      </Over>
      <Normal BackColor="#DDD9CD" Cursor="Hand" Font-Size="8pt" ForeColor="Black" Font-Names="Webdings">
            <Padding Bottom="2px" Left="0px" Right="0px" Top="0px" />
             <BorderSettings>
                 <Left Color="Black" Style="solid" Width="1px" />
             </BorderSettings>
       </Normal>
 </DropDownStyle>

Regards,
Handy