Does anyone know what this tree is and whether it is rabbit safe?

[~ILoveMyBunny~]

A tree we have in our front garden has suddenly grown huge this year. I want to cut it back but was wondering first if anyone knew if it was rabbit safe so I could give the branches and leaves to the buns?
I have a suspicion about it maybe being a type of willow but I'm not so great with trees.
Thanks!

 

[joey&boo]

Does / did it have catkins?

 

[Omi]

Looks like Goat Willow. Catkins would be reassuring.

 

[~ILoveMyBunny~]

Problem is I don't remember now.. We've got loads around, too many in fact. They've all doubled in size this year. I've seen some with catkins but some don't seem to get them. If it might not be safe I won't risk it.
Thank you both