Well first we should probably establish how cold the water is once it hits the ground. I imagine it is heated to almost boiling temperature in the Nespresso machine, however when it comes out and hits the cold cup it cools down almost immediately to probably 85 to 90°C or something around that.
In general colder water means basically that you are extracting less solid compounds of the coffee at a slower rate. So it is impossible really to draw any specific conclusions without knowing how hot the water is and how long the extraction takes.
However there are some general rules that always apply as the aforementioned slower extraction at lower temperatures. Another one is that with increasing contact time the extraction will be higher.
In terms of flavor lower extractions are generally associated with more acidic/sour coffee and the higher the extraction the more of the bitter compounds will be in your cup. An ideal extraction will be balanced with some fruity acidity and some darker, chocolaty flavors. Since you are using a full immersion technique it will not make that much of a difference though. I imagine you wait a few minutes before you start drinking the coffee? So there's probably a short moment where the extraction is balanced but the longer you sip on your cup the more bitter it gets which means overextraction. I think time is the more relevant variable in your case (if my estimate of the temperature is more or less correct)
Health wise I don't think it will make much of a difference either for the above mentioned reasons. Most of the caffein is extracted early on and by the end the extraction will be relatively high, regardless of the somewhat lower initial temperature. And since you are doing full immersion you will additionally always ingest a good amount of coffee grounds anyways.