I know nothing about golf, however…
I think that we are talking "major golf centre" as opposed to "centre of major golf courses".
There are many, many golf courses in the 'northern Mediterranean equivalent' zone across the US and Canada that are good courses and have good attendance.
I just had a look at the list of top 100 golf courses in Canada (of course, given my knowledge of golf that might equate to the bottom 100 in the world but I doubt it) and I can tell at a glance that there are very few near major airports. Sure, the best one, St George's, in Etobicoke, is only 6km from Toronto international airport but of the top 15 public courses in Ontario very few, if any of them, are near a major airport.
The population of Ontario is approx. twice that of Bulgaria. The land mass is 9 times, which implies a much higher population density in BG. However, I know that there are vast swathes of unpopulated areas in Ontario so, if you say that the population is spread across 1/5th of the land mass, that then implies a similar density to BG.
There are 471 (places with) golf courses in Ontario and there are 13 airports (not major international airports, thirteen airports with scheduled flights) serving that area that is 10 times the size of BG.
A, albeit quick, search shows six golf courses in BG (one in Ruse, with no airport), there may be more but, I think, it certainly demonstrates that the country can support more. Whether it could ever be a “major golf centre” is a moot point and I would probably say no.
You could say, with half the population, we could support 235 golf courses or with 1/9th of the area we could support 52 golf courses. If you were rude, you could say that with 1% of the initiative we can’t support any more.
Having said all that, there are probably a lot of other factors that determine the viability of golf courses but, again, I don’t think winter snow or the lack of an airport, going by Ontario as an example, are that much of a problem.