Can water freeze and snow fall in biomes in Minecraft?

In the current version of Minecraft, can water freeze to ice in tundra biomes, as it did in ice worlds before biomes were introduced?

Relatedly, can new snow fall in tundra biomes, after scooping up all the existing snow?

Now that it can snow again in snowy biomes, water can indeed freeze to ice after long enough exposure to snowfall. See the 0:15 mark of the linked video for an example.

In 1.5, coming out next week, snow will again periodically fall in snowy biomes, causing water to freeze into ice and replenishing the snow that you've collected beforehand.

As of Minecraft 1.6.6, water freezes and snow falls in icy biomes.

The top layer of water freezes in icy biomes, even when it is not snowing. Water will freeze even above sea level. (Although a development preview video prior to the 1.5 "Weather" update appeared to show water freezing, this feature did not work until Minecraft 1.6.)

As of the 1.5 "Weather" update, snow periodically falls in icy biomes as it did in old pre-biomes snowy worlds, and will form a layer of snow on the ground.