The important bit first...
My question for you is this: What does his pediatrician say?
During the first 5 years of a child's life is when the myelinization of nerves occur. The myelin sheath is the special coating that allows neurons/axons to send messages incredibly quickly (http://en.wikipedia.org/wiki/Myelin has some basic info on it). It is formed essentially out of lipids (fats) with a little bit of protein thrown in.
While in school studying neural physiology we were taught that children in this age range should typically NEVER be restricted in their fat intake from healthy sources.(IE...Always whole milk in preference to any percentage of skim, etc.) Of course, there's always medical exceptions. If your toddler isn't an exception...I would be THRILLED that the one thing he does want to drink is milk. I know mine typically drank about a half gallon a day. The water bottles with the straws and the coolers you pop in the freezer keep it cool enough to be fresh for several hours.
Less importantly, here's something I have (but most people don't) which MIGHT be the reason behind things...
It may be that your son is a "super-taster". I know I am, & I can't stand the taste of most kinds of water either...nor have I been able to my whole life. ESPECIALLY fluoridated water...it catches in the back of my throat and makes me gag. Every kind of "local" water tastes radically different, even within one state...cross regions (washington v. california v. louisiana v. etc.etc.)it's so different I don't even fathom why everyone can't taste it, yuck! Even each and every kind bottled water tastes different. My mother would have to make juice straight from the fruit if she wanted me to drink it (yep...can taste the flavor of water through juice), but milk was my staple growing up.
Anyhow, Food for Thought.
:)
Z.