It does sound culture-specific, so it may be worth mentioning where this happens. I have lived in several countries and no one has ever one this to me, and I didn't know people did it.
I'd have no problem with my friends stuffing cake into my mouth with their hands on my birthday! It's not a cultural thing in the UK but if my friends want to start it, great!
Then you are more than welcome to allow your friends to do such a thing. My friends can put cake on my face, but not my mouth.
Well, thanks for your permission! ;-) Personally, I'd be very disappointed if delicious cake missed my mouth and went all over my face. That'd be embarrassing in the middle of my birthday celebrations in a restaurant!