Can you put ice in your kiddush cup to make it full or if you just want it to be cold
It is permitted to put ice into the cup in order to make it full. However by putting the ice inside, you run the risk of diluting the wine, therefore it would depend on how strong or diluted the wine or grape juice is. Practically if it is put inside right before making the Kiddush, for the minute that it takes to say Kiddush, and the wine is already cold, I would assume that it wouldn’t really get diluted. In contrast, putting the ice inside to make it cold means that you do want the ice to melt into the wine, then you would have to be sure that the wine is strong enough that halachically it is permitted to dilute it more.
As a side point many wines and grape juices nowadays are diluted to the degree that adding even a little bit of water could disqualify it from being kosher for Kiddush.
M:B 182-19, Teshuvos M’bei Midrasha 26, Poskim.