Yes it is very natural to say this sentence without "on".

In spoken American English these prepositions are dropped regularly. It can sound a little abrupt, but not at all wrong. Let's meet again Tuesday. When's my next appointment? a. Tomorrow 9am. b. Friday the 3rd. Your next appointment is April 12th. On the 3rd of April, our reply is due. ("on" is needed here) Our reply is due (on) the 3rd of April. ("on" is optional) That said, I can't think of a case where it hurts to use the prepositions.

love it!

It is not totally wrong, but it's really casual :)