A little over a month ago I started shaving with cold tap water with surprisingly good results.
I have had consistently smooth shaves with ZERO razor burn.
My prep concisest of washing with a face cloth (no soap) period.

A couple of things to be aware of...
You need a Sharp razor!! At least a 1/2 hollow if not a full wedge to start.
You haven't heard noise until you try a full hollow on a cold beard!

Finding a soap or cream that will stand cold water. The best combo I've found is a brush of Mama Bear's Awakenings with a pea of C.O. Bigalow cream mixed in. If you like menthol this combo is for you.
I lather on the face and work well into the Beard. Use a little more water than normal. The lather has a tendency to dry out.

Give this a try. You might be surprised.