Is there any reason that I shouldn't replace the rubber on a DSLR with leather? I only ask because I like the older SLRs look and I have a Nikon D5200 id like to mod in some way. What issues should I be aware of if I attempt this?
I think the main issue is going to revolve around how you're removing the existing rubber on your camera without damaging the camera.
The second issue is getting new cover pieces that will fit perfectly with appropriate cutouts (say, for the infrared sensor on the front of the grip), and then which adhesive you're going to use to attach them.
Most of the pre-made replacements I've seen have been for restoring vintage cameras where the adhesive and the leather/vinyl have disintegrated over time, or for mirrorless cameras. I don't think I've ever seen a ready-made kit for covering a dSLR, like the ones for mirrorless offered by Aki-Asahi.
I don't see why not. See this question for advice on repairing the rubber grip, and if you're just looking to replace that (and if you're comfortable with working with leather in general), I'd say go for it.
That said, for considerably less effort, you might consider a classic leather camera case, like this one (chosen randomly from Amazon; not a specific endorsement). That covers and protects the whole camera (and a mounted lens) and flips open for easy use.