ANSWER:

No need for soap. It would be sufficient just to rub it with Water. 

if at night I apply oil on my feet & arms because of cold weather, do I have to wash it with soap before fajr to make sure the wudhu water reaches my skin? & likewise if I apply during day time. or is it ok to do wudhu directly on that oily skin?

Ablution (Wudhu) |