Yep all varities of willow are safe, there are over 200 species, the issue is that the levels of salicins differ between species, and also between younger and older growth.
However, no one really knows what levels of salicins could cause toxicity in buns... certainly buns with a bit of a wild instinct will often choose to eat willow if they have pain. Salicin being a starting point for salicylic acid (aspirin) a NSAID like metacam.
The farmer who grows my hay is also a specialist willow grower and he told me once to test the willow I give to my buns by chewing it myself first! :shock: If it makes your mouth go dry it's ok... if it makes your mouth die from the most disgusting parching dehydrating taste then the levels are probably too high to feed! :lol:. He suggested feeding young growth if possible. When they make their willow toys for buns he will peel some of the species first to reduce the salicin levels, but other willows he uses he will leave unpeeled for buns.