Amber college would nope right the fuck out. They love wild places. To them, burning down the forest to get rid of beastmen would be like burning down your house to deal with your roach infestation. Congratulations fuckwit, they're gone but you've destroyed everything important in the process.
Then there are the wood elves, who would pretty much kill you for so much as LOOKING at a tree funny. They have enclaves in the Empire's forests, and could probably call on the main group in Athel Loren if you started making any progress at all.
High elves would have nothing to do with defiling nature. They might even join up with their cousins in stopping you, particularly if you're not the Emperor himself.
DE keep on raping and pillaging because they don't fucking care either way.
Ogres help if you pay them, and eat you if you don't, so business as usual there, too.
Bretonnians would be leery of helping. Relations are good, but they've got their own fay in their own sacred wood, and they might be reluctant to do such acts even in another country. Besides, if the Empire got too strong Bretonnia could be in some serious trouble.
Dwarfs would theoretically be all for it, but in practice they've always got their own shit to deal with. Don't expect a whole lot of numbers, but maybe they'd donate a few flame cannon to the cause.
Skaven would, ironically, love this shit. Less forest and more towns means more places where THEY can spread chaos, mutation, and plague.
So, overall, it'd be a long and arduous slog that would piss off half your allies with no guarantee of success and at the end of it, you'd have just traded one rot for another.