Dartmouth also has a very active outing club (DOC) and it’s the oldest outing club in the nation.
Through the DOC, you can do so much (skiing, canoeing, etc) and the DOC provides any equipment you’d need. The incoming class also has the first year trips where freshman have the opportunity to bond over a 5 day camping/hiking trip before their start at Dartmouth.
Both Williams and Dartmouth are amazing schools. Do you plan on going to graduate school? If so, Dartmouth has amazing resources nearby and on campus that provides lots of opportunities and experience (DHMC, Geisel, Tuck, etc).