Australia - most snow lands in Southeastern Australia.
Snow cover may stay for 60 days over 2,200 km2 on mainland Australia and 1,200 km2 on Tasmania according to authorities. Snow cover may stay for 30 days over 7,938 km2 (based on 1,400 m altitude at 36 deg S) on mainland Australia. The only permanent snow Australia has is a few snowdrifts.
Switzerland has an area of 41,290 km2, of which 9,788 km2 is over 2000m altitude at 46 deg N. Switzerland has 1,230 km2 of permanent glaciers.
In terms of the question being asked, Australia has more snow-covered land in actual area.This is only during winte, and due entirely to the fact that Australia is such a vast continent that, even though there is relatively little area that is high enough for snowfalls, it still covers a greater expanse than that found in Switzerland. The areas covered by the Australian Alps, the High Country of Victoria and the mountainous regions of central Tasmania have significant snowfalls during winter, and their area covers more land than that found in Switzerland.