Front wing damage in this game is not very realistic. I have damage set to full and suffered some front wing damage in a race last night. My engineer told me to come in, but since it was a wet race my AI opponents were not exactly driving all that fast, I held on to my position driving with a damaged wing. If this had been the real world I would have had to stop.
If you lose all of your front wing, is almost impossible to drive fast...
I never lost it at a wet race, so I can't say if it has influence or not. Just know that if you lose just a part of the wings, the handling keeps almost the same.