Does Monk Unarmored Movement work on snow?

Monk’s Unarmored Movement says that at 9th level

[…] you gain the ability to move along vertical surfaces and across liquids on Your Turn without Falling during the move.

Is there anything in the rules or otherwise saying, if this should work over deep snow, same way it would work over liquid water?

I guess moving on quicksand or canvas tent/awning roof would be other similar cases, so anything covering this would help too. They’re not liquid and not vertical, so by the above quoted text alone, the monk would sink/crash/fall.

Is there anything better than "well, thematically it would fit and be so cool and not really unbalancing" to say to the DM when asking them to allow running on snow the same way as on water?