Will downloading ios 6, slow down iphone 4?

It depends what version of iOS you're at right now. Yes, you're likely to see some slowdown since iPhone 4 is less powerful than the A5 and A6 processors of the 4S and 5, but if you're already running 5.1.1-- you probably won't see an INCREDIBLE amount of slowdown. In fact, if you're going from iOS with a bunch of crap installed to a clean install, you might actually notice it speeds up some. Personally, though I thought the opposite would happen, iOS 6.x (upgraded from 5.1.1) actually *improved* my battery life pretty noticeably. I expected it to get worse. And, as I said... I went from an install of 5.1.1 with tons of apps and other garbage installed on it, to a clean restore, and it did not run any slower (that I noticed) than iOS 5.

If you're upgrading from iOS 4.x, then yeah, I would expect to notice a good bit of slowdown. It's all a matter of what version you're on, and if you're going to restore all of the same stuff back onto it, or if you're going to do a fresh restore and re-install only what you need from scratch.

So the answer is, mostly: possibly a little, but not by a huge amount. Hope that helps some.