Do most UI designers use Mac computers, rather than Windows devices, and if so, what things are specifically missing from Windows devices that make a Mac essential?

Echoing personal preference as the sole answer here. I'm sure you could even be effective on Linux if you really knew your way around it. I personally abandoned Mac OS ages ago because I found it obnoxious. Limitations to hardware upgrades back then were ridiculous. It could be different now. I built my first windows based machine (a pentium 75mhz! Imagine that!?) hand picking all the parts. I could customize it completely for me and I've never looked back since. But, I am a tinkerer and that's not for everyone. My laptop is my primary machine and it's a huge brick that started life as an iBUYPOWER an has since undergone a few upgrades. I love it. I'm not so sure I could so easily upgrade video cards in a MacBook Air. I do work around Mac users and I have never once ran into an issue that couldn't quickly be resolved. Now with so many cloud services that run in a browser like project management softwares, CRM, proofing systems, so on so forth it's completely not a problem to share my work with anyone on any platform. So, no difference as far as I'm concerned. Just preference.

A good way of becoming a better judge of quality is to surround yourself with quality in everything you do, and everywhere you go, and then discuss with others what makes it good. As a designer the tool you use the most is your computer, so the quality of that will have a big, if not directly perceived, influence on the quality you are able to produce. In my opinion Mac OS is better than Windows, and the build quality and design of any Mac is far superior to most PCs. That is the reason I use Mac.

There's no such difference, its only a matter of personal choice. As a UX designer all you need is some good and effective tools for getting things done and independent of your operating system. I have used both windows and mac and there's absolutely no difference I have encountered so far in my design process.

As far as tools go, there is very little difference - You can get the same powerful tools for either device. (Though I must admit: Macs display work in a much more pleasant fashion than PCs.) I went for years doing creative/design work on a PC and ppl assumed I used a mac to do it: However, in a collaborative environment there is an inherent system and means of display on a mac that a PC just doesn't have. Also, macs have the advantage of "critical mass" in the industry  - like a Creatives' Facebook. (You can start your own social network but everyone else is on Facebook so how can you work seamlessly with everyone if you're not on there too?) Unless of course they don't know you're not on the same system. Then I guess it doesn't matter ;-) - no difference.

A good UX designer can use paper to get the job done! Most UX folks I know prefer macs because the user experience is arguably better and it has Omnigraffle. I've used both in the past but haven't touched a PC for about five years. Tools like Axure  and Office are cross platform and I can do a lot using google drive / docs. p.s. UI is not UX, just part of it.

Can't answer this question directly since I am not a Mac user, so I will be answering this from the point of view of a Windows user. Like most people have already said, I think it mostly comes down to preference. I have always been a Windows user and partially a Linux user for work. I prefer working in a Windows machine because of the software I am used to working with is available there. I am restricted to Linux at work because it is what's provided so I just make the most of what I have. I would say I'd work faster in a Windows machine while in a Linux, the quality would be the same but it might take a bit longer because I am not used to it.