I would assume so, as Cabal Stronghold counts basic swamp cards, and Snow-Covered Swamps have both basic and swamp on the card type.
Yes, the snow-covered lands do count as basic lands.
205.4c Any land with the supertype “basic” is a basic land. Any land that doesn’t have this supertype is a nonbasic land, even if it has a basic land type.: Cards printed in sets prior to the Eighth Edition core set didn’t use the word “basic” to indicate a basic land. Cards from those sets with the following names are basic lands and have received errata in the Oracle card reference accordingly: Forest, Island, Mountain, Plains, Swamp, Snow-Covered Forest, Snow-Covered Island, Snow-Covered Mountain, Snow-Covered Plains, and Snow-Covered Swamp.