Yes rabbits can eat willow.
I regularly give ours some.
However willow does have a type of aspirin in the bark (in fact it was the original basis of aspirin) and I would say not to give more than a couple of handfuls at a time as I did once have a bun who had a a touch of stassis after a lot of willow and I wondered if the aspirin had affected the stomach.
They can have them either fresh or dried