It could be a crazy idea in so far as a donkey would be struggling to pull a finger bar mower. You may need a team of donkeys, or a pair of Fell or Highland type ponies, or one decent sized horse.

Remember, with an equine (or two)(or more), it is imperative that you have time to feed them, muck out their accomodation, and train them. Then there are the costs of worming/worm counts, shoeing, tack/harness, vet bills, winter feed...
If you buy a decent tractor, you need only put diesel and oil in it and, if looked after, it shouldn't cost you an arm and a leg. You don't have training or daily maintenance, and can turn the engine off and forget about it till next time it's needed.
Personally, I would rather work the horse(s), but sometimes there just aren't enough hours in the day/week/year.