Based on my 16 years of collegiate racing and coaching, I feel compelled to chime in:
Divisions I/II/II refer to the NCAA, and dictate rules (for recruiting, playing season length, scholarships, etc.), not ability. About 40-something NCAA school sponsor varsity skiing. A few schools in the NAIA (an alternative to the NCAA, with looser rules overall) also sponsor varsity skiing, plus a few Canadian schools (don’t know what their nat’l ass’n is called, if any), and in the past a few NJCAA (junior colleges) have sponsored varsity skiing (don’t know if any still do). Sierra Nevada College has also sponsored a varsity ski team, and at least until recently had no affiliation with any of the aforementioned national organizations.
Since so few schools sponsor NCAA skiing, schools with different divisional affiliations compete against one another, and the NCAA holds a single National Skiing Championships, with all the divisions jumbled together. Schools like UVM, Dartmouth, Boston College, Brown, UMass-Amherst can make a semi-legitimate claim to have Division I ski teams, since the schools are Division I, and they sponsor varsity ski teams, although they compete mainly against Division III schools. By contrast, such powerhouses as Williams, Middlebury, Colby, Bates are all Division III, despite their confused and misleading claims to the contrary. (Division III schools can elect to designate one of their sports to compete at a different Division level - some smalls schools in the Boston area do this in hockey - but nobody has done this in skiing, especially since it would make no sense as skiing competition is not segregated by divisional affiliation.) When I complained to the NCAA that Division III schools were making entirely illegitimate claims to have Division I ski teams, their response was that not everything that is wrong and misleading is prosecuted by the NCAA.
About half of the NCAA varsity ski teams are also affiliated w/ the USCSA (called the NCSA back in the 80s), which is sort of an umbrella organization, offering a national structure for varsity ski teams that are NCAA, NAIA, NJCAA, Canadian (despite the US part of USCSA), and unaffiliated (Sierra Nevada) as well as for club teams, which represent the majority of USCSA membership. Club teams are not Division III, as that refers to a category of NCAA membership, which has no bearing on non-varsity programs at NCAA schools.