I have mostly drunk cold water on my fasts and not felt any ill effect from it. I respect those that say no cold water and the reasons for it, but if we look back to nature as we often do and should in these cases, natural water from rivers and streams in many climes is cold to drink and all animals drink from them all the time. I don't have a problem with it. I do think we get 'addicted' to cold drinks it's true I certainly have been, and certainly there is a good reason to not drink fruit juice cold as it changes the active nutrition content. But there is no nutrition content in water and I don't believe it takes much effort to warm it to body temperature, but that's just my opinion. I have been juicing warm lately and have found my desire or need to have cold drinks including water greatly lessened anyway and I do think that's a good thing.
So don't stress about it. Take the advice of cold water on board but I certainly see it as optional, it's up to you what you decide it shouldn't effect the fast greatly either way.