I don't think anyone can give a definite answer to that question.
I suspect that simple melee combat is the most played. It seems the easiest play style.
Sneaking is fun. The Thief series of games were some of my favorite games. I played a rogue in WoW for years. But in Skyrim (and Morrowind and Oblivion) I didn't do a lot of sneaking. I don't know why. I feel sneaking a little too easy (overpowered) in Elder Scroll games. When you have low sneak skills, the mobs will always see or hear you, no matter what you do. Then when you level up sneaking, or get some strong enchant on your boots, suddenly you can sneak by everyone and everything.
Also, sneaking works less good when you have to attack multiple targets. Also, sneaking with a companion feels awkward.
I never play a magic character in RPGs or MMORPGs. So I can't tell you much about it. But the magic style still seems to have a lot of followers.
If we had to guess which style is most populair, I would guess an archer. With or without stealth. I've seen so many videos on YouTube where people exclusively use their bows. I have 2 friends who play(ed) Skyrim, and they prefer bows too.