Is it realistically possible to own a small farm and work as a nurse practitioner?

Why not? Nothing is impossible.

Some things to consider--

What shape is the farm in? Does it need fixing up, or are things in pretty good condition?

What kind of help/support is available? Are there other family members who can make a contribution, or will everything fall on you? Can you hire someone at a cost-efficient rate to do some of the labor for you?

What kind of flexibility will you have with either job?

Will you have animals to worry about? You should probably have a back-up plan if you have any kind of livestock.

Seems like this could work well for you. If you have a fair amount of autonomy in your practice, you might be able to barter your services for help with the farm--tilling, fence repair, vet services, etc.

Please, keep us posted on your progress. I wish you the best.

I have nothing of substance to add, but have to ask: would this be a "country doc" type of situation, i.e. rural practitioner? I think that would be pretty cool.

As another noted, a lot would depend on just how much work this farm would take. I have no idea how what kind of commitment that takes.

One thing to consider is that you may not be able to start immediately in just any nurse practioner role out there. Many NPs start by being hired into a group practice where they get the experience they'll need to move forward with their practice. The location and hours may not be your ideal choice. So you might want to get more info on what kind of NP you're interested in and what the job market is for both inexperienced and experienced NPs in your area. That can vary a lot from place to place.

Once you've got a firm foundation in the area practice that you're interested in, then you might be more able to get the kind of flexibility that some NPs have. Keep in mind that you'd also likely be on call at all hours of the day and night, meaning that you might need to drop whatever it is you are doing to go take care of a patient.

Just food for thought! It may be different in more rural areas.