Context is everything here:
Is the ONLY issue here that you're upset that he didn't run it by you first? If so, then you're not overreacting to be annoyed. If dog-sitting won't impose any true hardship on your home/life then I would just let it go and not fight about it, but remind him to ask you first next time. But if it's truly going to be a hardship to watch the dogs (especially if it means YOU will get stuck with most/all of the caretaking and cleaning up) then you're within your rights to tell him that the ex should hire a dog-sitter instead.
Or is the issue here that you're upset that he's doing a favor for his ex?
- If he's not in regular touch with the ex and if this is an out-of-the-blue favor request - especially if the dogs belonged to both of them during their marriage (as opposed to the wife getting these dogs on her own after they broke up) - then you're overreacting. It's not unreasonable for her to ask someone she trusts with her dogs to watch them, especially if the dogs were once his.
- But if the real issue here is that he's way too friendly with the ex for your liking - especially if they don't have children together (because if they DO have kids then it's reasonable and beneficial that they have at least a cordial relationship) - then that's a separate issue from the dog-sitting and you need to determine if it's truly a boundary issue or if it's a matter of you being insecure about their truly innocent friendship.
Your husband being on friendly terms with his ex-wife is not, in and of itself, an issue. But if their relationship is inappropriately close, then you have a point.
Figure out the REAL issue here, then talk to your husband about it calmly, see how he reacts, and from there you can move forward.
ETA: Reading your updates, it seems like he has a real problem with drawing appropriate boundaries with his ex, and also with letting her go from his life. I'm baffled as to why you married him knowing full-well that he still keeps his ex in his life to this degree. Being on friendly terms because of their son is reasonable, but keeping her on his bank account and volunteering YOU to do favors for her is unacceptable. Marriage counseling would probably be a wise idea.