Freezing effect applies to player in snowy biomes under certain conditions.

The requirements:

It would have to be nighttime and the player would have to be in contact with a snow/ice block/layers.

Or

It would be daytime and the player would have to be in contact with a snow/ice block/layer during a storm.

Or

Submerged in cold oceans and rivers.

Even if these requirements are met there would be various ways to negate them.

Standing by a campfire or other heat source (especially nether campfires) such as a few torches, fire or lava or leather armour.

This would I think provide a unique challenge to surviving in a snowy biome but not without ways to avoid it.