My biggest concern would be that the care instructions for the jacket (generally dryclean) would contradict the care instructions for the print. I have no idea what happens to the print on a screenprinted jacket when you dryclean it... maybe nothing, maybe it gets destroyed.
So yes, you definitely can print on a woolen jacket, but the thing to find out would be if there's a way to wash the jacket that doesn't harm the jacket or the print.
Also, given that I've seen screenprinted vintage jackets on the market (including a mashup of a vintage jacket and a hoody I saw just today at Kmart) I'd say there probably is some kind of combination of elements that would work, you just need to find out which one.
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