In most (probably all) Western European countries, OMFS is really a "medical specialty" with dental roots...
As someone training in Europe I'd like to comment on that. There are big differences between countries. The general rule is that the further south in Europe you go, the more MD oriented OMS becomes. In many southern European countries OMS is a medical speciality with only a few OMSs having a DDS/DMD as well.
Because the countries within the EU are trying to establish a common training pathway for OMS, there is a dental element to OMS training in all EU countries, but it varies from a non-clinical course of 3 or 4 months duration to actually sitting through the later years of dental school and earning a DDS/DMD.
In the northern part of Europe (for example UK, Germany, Swiss, Austria) OMS is more dentally oriented, but it requires a medical degree. In this part of Europe, most OMSs go to dental school first, then med school but doing it the other way around is not uncommon Few European countries have the same well structured recidency programs as the US, with med school integrated into the program. I think Holland is the only exception. In most European countries future OMSs will have to put themselves through med school and dental school first and then apply for recidency, but once you have the double degree, you're pretty much guarantied a spot in recidency.
Those doctors that are "oral surgeons" in Europe without medical degrees are really some sort of mix between "exodontists/hospital dentists/implantologists/periodontists."
This may be true in the southern part of Europe.
In the Scandinavian countries (where yours truly is training) OMS has basically the same scope as OMS in the US. It is a dental speciality, with no obligation to have done med school.
I'm afraid I'm not much help when it comes to requirements. I'd assume you'd be able to get a dental licence in most of the Scandinavian countries, but you'd probably have to sit through an exam. Maybe take a short course at a dental school? You
would have to take a language test.