I sure do agree with Ursula, watering with ice cubes isn't going to benefit a tropical plant (which most indoor plants are) let alone an orchid.
The shock of ice cold water will certainly slow down the plant's growth, and may actually induce dormancy in some really sensitive plants. Inside your house where your plants are happily growing at 65 to 75 degrees, why would you water them with 32deg. water?
I've used ice cubes to keep some plants cooler in my Florida garden, when the weather warms up too fast in spring. Cool season veggies don't mind the cold water. Hardy perennial plants in containers outdoors might be ok with ice cubes, too, if you wanted to keep them dormant. Aside from that I can't think of another plant I'd ever use them on.