There are definitely nice freeride opportunities on the Falkert. The terrain below the Falkertspitz is even designated as a feeride zone. The variant descent via the Sonntagstal is also recommended. The Heidi Alm Falkert is also a good starting point for ski tourers.
Those who are not yet confident enough to ski in the terrain alone can also explore the deep snow area together with a ski touring guide or freeride instructor.