I live too far south to fly on skis now, but when I lived in St. Louis I logged many many hours of snow flying with a variety of aircraft. Folks tried all sorts of weird spring loaded pivot mechanisms, rubber bands, fishing line, etc. etc. At first I tried several pivoting designs too.
None of these designed really worked and I eventually converted every other flyer over to my simple and greatly improved design. I simply bolted the ski rigidly to the landing gear with no ability to pivot at all in the case of sheet aluminum landing gear legs. With wire gear legs, where fixing the angle was more difficult, I stabilized the skis with taut wires fore and aft.
The key to success is fixing the angle of attack. The ski should be roughly level with the snow when the aircraft is in the landing/takeoff attitude without any tendency to pivot.
There was no tendency to tip over or dig in either on hard of soft snow.
I made my skis out of two layers of 1/64" plywood, laminated with the curved nose area formed over a pipe. Then I applied MonoKote to make the bottom slick and smooth. These days I would 3D print the skis.