A trade war, even if we aren't the one's starting it, will hurt both countries.  The only countries that benefit are those otherwise uninvolved (China, Germany, Japan, Korea, etc. in this situation).

Trade wars are pretty much universally a lose-lose situation for the participants.

Of course the solution to this "softwood lumber" dispute is EXTREMELY obvious: Have a fair, open and transparent bidding process for stumpage fees.  Government gets more money for the resources and the U.S. softwood lumber industry loses their only leg to stand on.  Our lumber would almost certainly still be substantially cheaper than that of the U.S.