It is really unnecessary to freeze your water just to prevent the lye water from getting hot. Lye water will get hot, and it's not a big deal (I mean, I've never seen it boil or do anything crazy before). I have used a 1:1 ratio of lye to water and added sugar 1 TBS ppo, watched my water get nice and amber colored (and hot as a pistol!), and it was fine.
In fact, you wanting to freeze water just to make sure lye remains cool could cause more problems than not. There is always a chance of having lye crystals undissolved when using a slushy. A lot of people strain there slushy lye mix to prevent crystal from ending up in there finished product. Having to do this constantly could prove more hazardous than just mixing lye with regular temperature water. For a full milk soap, I understand, but for regular water soap to do this everytime is truly not necessary.
Now if you're adamant about cool lye water and don't want to mix it hot every time, you can master batch your lye one time and it will be room temperature after the initial mix. I really don't know if I'd recommend this to a brand new soaper until they fully understand the entire process and ratios of lye to water, adding things back, measuring etc etc. I threw that out there because I am not positive how new you are or how much you already know. I also wanted to throw that out there for any new soapers that might be reading this.