Caveat lector: First of all, this is super rambly because I'm at work right now and it's 3 AM, so please ignore typos or any advice that sounds like I pulled it straight from a different universe or something.
I'm not sure if I'll be super helpful because my program isn't online, but I know MN has a very solid mostly-online MPH program (I think they make you come for some in person stuff during part of a summer or something?).
For me, personally, I don't know if I would want to do all of the work of an MPH
at the same time as vet school, if that makes sense. Masters programs are very oriented toward lots of reading and thoughtful processing of information and I feel like the workload of MPH coursework on top of the stress/huge workload that is veterinary school may not always be a fun experience. It's definitely doable, but for reference I just printed my weekly readings for my MPH coursework like five minutes ago and it's easily over 100 pages front and back for my four MPH classes. I'm expected to be able to discuss these readings at length, so I will often read many of them several times, make notes, look up supplemental information, etc. Toss in things like papers, exams, presentations, projects, and homework, and it can turn into a very formidable workload very quickly. (side note, this semester is much more coursework intensive for me than last semester, mostly because I'm taking a lot of policy and epidemiology classes, which will both make you read until your eyes bleed. I still had a decent amount of work last semester, but weekly readings were closer to ~25-50 pages front and back)
(I also am just talking about me personally here, but I'm a wreck and can not be trusted to do self paced online coursework. Most other people have much more discipline and fortitude than me so this note is an entirely personal one
)
That being said, those MPH programs aren't bad and are a great choice for lots of people. I know I prefer having some division of classwork/degrees so I'm not doing everything at once (because I tend to do poorly when I make myself work like that), so having the 5 year program I'm in worked well for me because it allowed me to divide my coursework while still finishing up the MPH + DVM faster than if I had done them separately. Again, this is personal preference. If I were to do an online program I would probably shoot for something I could do over the summers or during breaks, but would be slightly apprehensive about burning myself out just from doing school essentially year round. Self paced stuff is good so long as you know you'll finish it and won't put off a semester's worth of work until the day before everything is due (aka be me). It gives you more flexibility, but at the cost of putting more personal responsibility on your own shoulders for keeping up with things.
Something I'll also toss in is that a huge chunk of people in my program now are vets, and most of the time I feel like they have much better perspectives/grasps on a lot of the material we learn purely because of that background - there are definitely some things I struggle with because I'm just not there in my schooling yet, and I think in some ways it's advantageous from a learning perspective to come into an MPH program having already had a background in veterinary medicine/practice. A few of the vets also practiced in public health fields without an MPH for a while and their workplaces were willing to pay part of their costs obtaining the MPH, which is a cool thing.
Also, as an aside, whoever told you they study 70-80 hours per week for veterinary school is probably dead now.
Don't study that much unless you've somehow managed to discover a way to convert pure suffering into more hours in a week in which you can sleep.
Um, anyway, something in the wall of text above may be useful. If you have any other questions or just want to talk shop feel free to PM me too!