Well, it depends on what type of role do you want. Do you want to be a full-time firefighter/EMT? If you do, then it's probably going to be hard to be an active firefighter/EMT and trying to get all your nursing classes done mostly due to the limited choices of when to do clinicals.
However, many departments are volunteer and you can manage nursing school and volunteering easily. You should also be able to manage a part-time firefighter/EMT position. However, some departments are starting to push for paramedics for even volunteers. These departments seem to be in areas where there are a bunch of EMS schools though.
Like realistically, get a part-time position, paid on call, or per call and it shouldn't an issue with being a firefighter/EMT and the schooling you will need to get.
I also know of firefighters/paramedics who later become nurse practitioners or physician assistants after they retire from full-time firefighting.
On my combo department, most of the firefighters have other jobs like teaching EMS students, patient care techs, flight paramedics/nurses, and ER nurses. They usually are not full-time though since they rotate every 3rd day.