Farming in a snow biome

Cover the water with wooden slabs. This looks nice, and lets you walk around without stepping on the dirt, e.g. when growing wheat.

Note that the melting effect of a torch has a limited range:

Torches also melt nearby snow and ice, making them useful to keep skylights from being snowed over and lakes from freezing in snow biomes. The torches will however only melt snow and ice from a radius of 2 blocks from the torch.

It's likely that you are placing your torches around your sugar cane farm, and thus the ice blocks in the middle are too far from the torches to be melted.

As an alternative, glowstone blocks have a slightly wider radius of 3 and could be placed in the air space above the water:

Based on gnovice's information, you can keep your Sugercane farm layout with a minor change. Replace every 3rd sugarcane block in the center row with a torch. This way, no block of water is more than two squares (three cubes) from the torch.

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Try putting glowstone under the water. I used this to keep a Venice like water road melted through a snow biome. It seemed like ice no longer even formed.