This works, the spell water walk defines snow as a liquid for mechanical purposes.
Water walk says:
This spell grants the ability to move across any liquid surface--such as water, acid, mud, snow, quicksand, or lava
Here snow is described as a liquid for mechanical purposes. I argue that this demonstrates that for mechanical purposes, the rules are respecting snow as a liquid.
Thus, I conclude that Unarmored Movement does work on snow, as snow is elsewhere described as a liquid in a mechanical context.
In the comments Mark Wells raised an objection worthy of consideration. He writes,
[Water walk] provides that list for the purpose of the spell it's describing. The context is that it's explaining how water walk works, not providing a general definition of the word 'liquid'.
My argument relies on an important assumption, based on the "Spells only do what they say they do" principle: a spell only changes the mechanical nature of something if it says it does. Else, we assume the nature of the thing is used consistently within and without the spell's description.
An example of this can be seen in the spell storm of vengeance. The effect during rounds 5-10 of storm of vengeance state:
Gusts and freezing rain assail the area under the cloud.
Under normal circumstances, environmental phenomena such as wind and rain do not require a caster to make concentration checks, unless the DM determines they should. Storm of vengeance specifies a change in the nature of this mechanic when it says:
The wind and rain count as a severe distraction for the purposes of maintaining concentration on spells.
The spell description specifies that we treat the nature of wind and rain differently for the purpose of the spell.
Therefore, since water walk does not specify that we are respecting snow (or any of the other terrains listed) as mechanically unique for the purposes of the spell, we conclude that the rules are consistent in their treatment of snow both within and without the spell description of water walk.