@jmorth, that is a Phalaenopsis aka "Moth Orchid". If there is no label with the plant you'll never be able to put a name to her. Phal. have been so hybridized by large commercial growers (who sell to the big-box stores) over the last decade or so, that there are now hundreds of varieties (perhaps 1000's
).
First thing you need to do is never, ever put ice on your orchids. Would you like your feet to be immersed in ice?
Secondly, your plant may well be in sphagnum moss and that is far too water-retentive for most (beginning) growers to deal with. Re-pot your plant in orchid media, and you can purchase a small bag at any big-box store. Get the Phal. mix. Thirdly, be absolutely sure the pot your orchid is in has plenty of nice, big drainage holes. You don't want your plant to have wet-feet. 90% of orchids are killed by over-watering, so when in doubt, wait a few days before watering.
In my hands, Phal. are a bit more difficult to grow than the vast majority of orchids. I prefer the Cattleya Alliance.
Good luck.