No, that isn't pickled ice. That would be difficult to manage. Ice tends to melt into water which makes the brine to dilute. These are called ice pickles because they are soaked in ice water to keep them crisp. It works, too. These slices stayed nice and crisp even after processing. They've got a nice mild sweet flavor, too.
This one is also from my awesome pickle cookbook.
1 quart cucumber slices
1 small onion, sliced
1 T. mustard seed
1 t. celery seed
1 c. vinegar
1 T. pickling salt
1 c. sugar
1/2 t. turmeric
Place cucumber slices and onions in a large ceramic bowl. Cover with ice and cold water. Place a plate over the slices to keep them submerged. Let them sit for 2-4 hours.
Drain the slices. Pack into pint jars, it should make two. Divide the mustard seed and celery seed between the two jars.
Heat the vinegar, sugar, salt, and turmeric to boiling, stirring well to dissolve the sugar. Pour over the pickle slices until jars are full.
Seal and process according to your altitude. I processed my jars about 10 minutes, I'm at 400 ft above sea level.
Let them sit in a cool, dark place for at least a month before enjoying.