Does "Mountainwalk" imply "Snow-Covered Mountainwalk"?

Question

If I am playing a deck with Snow-Covered Mountains, does a creature with Mountainwalk become unblockable or do they require Snow-Covered Mountainwalk (where "mountain" is interchangeable with plains, islands, swamps, forests and mountains)? Conversely, if I had a creature with Snow-Covered Mountainwalk, is it unblockable if an opponent has only regular Mountains in play?

I lack the experience with the Comprehensive Rules to be able to conclusively go one way or the other.

702.12a Landwalk is a generic term that appears within an object’s rules text as “[type]walk,” where [type] is usually a subtype (as in “islandwalk”), but can be the card type land, any land type, any supertype, or any combination thereof (as in “snow swampwalk” or “legendary landwalk”).

702.12b Landwalk is an evasion ability. A creature with landwalk is unblockable as long as the defending player controls at least one land with the specified subtype and/or supertype. (See rule 509, “Declare Blockers Step.”)

I suppose the question boils down to this: is "Mountain" a supertype of "Snow-Covered Mountain"?

Answer 1

Yes.

Since Snow-covered is a land supertype, and mountain is a subtype, a snow-covered mountain is also a mountain and thus plain vanilla mountainwalk applies. The land subtypes are specified in rule 204.3h

204.3h Lands have their own unique set of subtypes; these subtypes are called land types. The land types are Desert, Forest, Island, Lair, Locus, Mine, Mountain, Plains, Power-Plant, Swamp, Tower, and Urza's. Of that list, Forest, Island, Mountain, Plains, and Swamp are the basic land types. See rule 305.6.

However, you are correct about the converse. A creature with Snow-covered mountainwalk would be able to be blocked if you had a mountain but no snow-covered mountains.

Answer 2

Yes,

What can Landwalk through what is covered in 702.13c

702.13c A creature with landwalk is unblockable as long as the defending player controls at least one land with the specified subtype (as in "islandwalk"), with the specified supertype (as in "legendary landwalk"), without the specified supertype (as in "nonbasic landwalk"), or with both the specified supertype and the specified subtype (as in "snow swampwalk"). (See rule 509, "Declare Blockers Step.")

This is equivalent to

A creature with landwalk is unblockable as long as the defending player controls at least one land that has:

1. the specified subtype (as in "islandwalk")
2. OR the specified supertype (as in "legendary landwalk")
3. OR does not have the specified supertype (as in "nonbasic landwalk")
4. OR with both the specified supertype and the specified subtype (as in "snow swampwalk")

In your example a creature with Mountainwalk has evasion due to a Snow Mountain due to condition (1).

Your second example is not viable as a creature with Snow Mountainwalk can only evade through a Snow Mountain due to condition (4).