I have built a topbar hive (to Phil's design in this book) and have had a colony of bees in it for 9 months. I also keep regular hives.
The colony survived one of the coldest winters ever - with the open mesh floor open to the elements. Proof (if any were needed) that bees don't mind cold. It's damp that they don't like, and the OMF certainly provides a lot of ventilation.
But .... I have some practical issues with the design.
1. Despite being exactly to the spec, the bees built comb across the bars and stuck it to the side of the hive inside. This means that that comb cannot be removed to be inspected. If you are unconcerned about whether your bees are a source of disease for other hives in the area, this is fine. But a conscientious beek should do their best to ensure a healthy hive - and you can't do that if you can't remove the comb for inspection.
2. Despite the use of a circular saw and really careful construction, it's a bit tricky to get the internal end-stops to be bee-proof.
3. If you want to treat for varroa (and most beeks do), it's not easy because there is no top-bee-space on which to put the thymol (a natural substance, before anyone gets too excited.)
4. For the same reason, it's quite hard to feed the bees. You need to be quite ingenious and adept at handiwork.
Summary. Topbar hives are best undertaken by skilled woodworkers and skilled beekeepers, not beginners. And if it's honey you're after, go for regular hives.
My top bar colony died. It was the only colony that I was unable to treat for varroa and it was the only colony that died. Anecdotal, rather than convincing scientific, proof of my previous review.
I am interested that most positive reviewers have not actually kept bees!
I really do have an open mind and I love to try different methods, probably before I am proficient enough to do so.
I expect there to be a backlash against top bar/Kenyan hives because they are more difficult to manage than conventional hives. So new beeks will find that they have more dead colonies that their conventional colleagues.
But if your Darwinian goal is bees that evolve to resist varroa, then your dead colonies will contribute to evolution of the european bee. Good luck with that! You will need a lot of patience and a long life :-) And a lot of dead bees.