I know the plants aren't really big enough to be drinking much water right now, so you don't want to dilute your
nutrient solution as the ice melts. But when they get bigger and start drinking up more water, you can just replace the water their drinking daily with ice blocks. That at way you can do both (add ice and water) at the same time, thus help keep the nutrient solution cool, while topping off the water volume.
P.S.
Depending on how much ice you add daily (frozen water volume), you may want to pH adjust the water before you freeze it. If not, it can change your nutrient solution pH. Depending on the pH of the water source and volume of water your adding in ice daily, it can change the pH fairly quickly. If you pH adjust the water before you freeze it, you won't have that problem. To make it easier, I'll pH adjust about 5 gallons of water at a time, then freeze it a few blocks at a time (using cleaned out butter or whip cream tubs) until I'm out of room. Then just use the ice blocks as I need them, and their already pH adjusted. There's been a few times I have even frozen nutrient solution, so when I added the ice it also added some more
nutrients to the reservoir. I did so because I wanted all the water I added back to be ice because I needed the cooling effect, but I also wanted to add some nutrient solution back as well. So I just froze it first.