There are a number of variables that need to be taken into account.
Immediacy: People are breaking bones and catching colds kinda all the time.
Education curve: Combat medics can be trained comparatively quickly, but they require support. Full surgeons require a minimum of 4-10 years depending on whether or not you want to risk throwing out the benefits of residency.
Transport costs: It's cold, it's north, and blizzards are not conducive to transportation.
Equipment: And your average village of 300 can't support the cost of an MRI anyway.
Step #1: Demographics rule the first day
You have a limited resource. Your country can't survive with lots of happy 300-person villages. Its your industrialized centers with government and education (which are usually the largest populations during the 90s) that are first. You don't tell us exactly, but let's assume one doctor per 1,000 people.
That's 700 doctors for the nation. You must protect your national assets, so 2.5 doctors per 1,000 people in the higher density populations, spread the rest around. At a guess, one doctor for every 6-8 villages.
This is most sensitive to transport, especially where inclement weather is concerned, but we're talking bush doctors here (planes, cars, trucks). Note that by the 90s the majority of your nation will have a reasonable transport infrastructure — it's really an issue of how much of it was destroyed by war and how much of your repair and maintenance infrastructure went with it. So your real problem is helping people who can't wait 2-4 weeks to see the doctor, or (worse) can't be helped without equipment located at a central location.
This is a 60% solution. You'll have people die due to lack of sufficient medical care, but that's what will happen.
Step #2: Triage Education
Each village is expected to send 1-2 people for immediate basic-care training. These folks don't learn about medicine per-se other than first-aid (bone setting, wound cleaning and stitching, very basic illness care). Their predominent purpose is to oversee welfare: clean drinking water, good sanitation habits, etc. Stuff of a preventative nature. This is 6-12 months of training to relieve the stress on the bush doctors.
Step #3: Medics/Physician Assistants/Certified Nurses Assistants ASAP
Thankfully, the proverbial 80%1 of doctoring is made up of cuts, bruises, broken bones, and "basic" illnesses. Panicked 1st-time parents are frequent customers. The vast majority of this kind of doctoring can be dealt with using what in emergencies would be much-simpler-to-train combat medics, PAs, and CNAs. This would minimize the need for doctors to visit the remote areas all the time, leaving them free to focus on the more critical issues that demand their education and experience. These folks would most likely be drawn from your population centers and farmed out to the remote villages on a "we'll pay you a bonus for your sacrifice" plan.
Expect (mandate) that each village supplies 4 people for immediate and intensive training. One general practitioner, one PA, one RN, one CNA. What would normally be 4 years of medical school, 3 years of residency, and 2 years of specialization is now 2-3 years of school and 0.5-1 year of residency. Yes, that kind of cramming comes with a price, but it bumps you from 80% of the solution to 90% of the solution.2 So, within 3-4 years of the "epoch" you have most of your doctoring back in place.
Step 4: Equipment & logistics...
Now that you have the people in place, you need pharmaceutical distribution, hospitals, places that need equipment, warehousing, and other logistics. You can draw the people you need from the locations of the (probably) regional healthcare centers. This will include pilots, administrators, everything down to janitors and security. This is the bulk of your redevelopment. Even assuming some of this infrastructure was still in place, it will have needed repair and renovation. At best, 8-15 years.
I've made some outrageous assumptions, not the least of which is that a war that knocked off so many skilled surgeons didn't also destroy the truck drivers, warehouse workers, office labor, pharmaceutical manufacturing, and everything else that a very complex 1990s medical industry needs to operate. It's not just the handful of people at the tip of the iceberg (doctors) that you'll need, it's the 50-100 people (minimum) each needed to support them. I'm basically ignoring this other than Step 4. If you must rebuild the entire medical industry from a minimum condition, you're "national healthcare" will be set back to the 1880s. What few doctors exist may know a lot about what to do, but they won't have access to equipment, supplies, and medicine.
1 You know, 80% of the work takes 20% of the time.... I'm using the same kind of generalization.
2 You know, 20% of the work takes 80% of the time.... I'm using the same kind of generalization.