Parrots sitting on shoulders do not freeze in powder snow

The bug

When a parrot is sitting on the shoulder of the player and the player walks into a block of powder snow, the parrot does not take freeze damage.

How to reproduce

1. Summon and tame a parrot by feeding it seeds
2. Poison the parrot by running the command:

   /effect give @e[type=minecraft:parrot,sort=nearest,limit=1] minecraft:poison 100000 1

   This will make sure you know if/when your parrot takes damage.

3. Poison yourself by running the command:

   /effect give @s minecraft:poison 100000 1

   This is so you know when your parrot would die if this bug was not present (it should die at the same time as you).

4. Wait until you have a half heart left of health and your parrot stops playing damage sounds, then pick up the parrot by walking to it
5. Walk into a block of powder snow at your eye level
6. Wait until you die
   Respawn, and notice how the parrot is still alive

Relates to MC-115048.