Watering house plants or any tender tropical plant (which most indoor plants are) with ice cubes is a very bad idea.
Plants growing in the regulated temperature of a house are suited to temperatures of between 60 and 80 degrees or more! It is generally recommended to use room temperature, or even warm water to water these plants. Cold water will shock the plant, and could even induce dormancy.
In my garden in Florida, we occasionally have night temperatures that dip into the 40's and very rarely into the 30's. Everything goes dormant for weeks if not protected from the cold, and many plants die off because of the cold temperatures. The only plants I ever water after the nights have been cold are the cool weather vegetables like lettuce, cabbage family, peas etc. The rest get covered with blankets through the cold nights, and watered with warm water after the day warms up to keep them growing.
