Your floor plan size of 4’x6’ will be tight for [2] people, with their “personal” gear.
4’x8’, with door in the middle of an 8’ side (allows equal egress), would be probably be a better choice.
Due to the small size, weight could shed weight by using 1x2 intermediate wall studs and 1x3 (made into an L) for the corners. I made a deer stand of 1x2 and 3mm marine plywood. It lasted over [10] years outside, with no maintenance. It’s easy to over build a small shelter.
Check posts about “runners” freezing in the ice.
General Material Weights:
1/2” Treated Plywood @ 1.42 ppsf (45.5 lbs per 4x8 sheet)
2 in. x 2 in. x 8 ft. Furring Strip ≈4 lbs
2 in. x 6 in. x 8 ft. Stud ≈16.6 lbs
1/4" x 48" x 96" sheet of LAUAN weighs ≈17.5 lbs
R-6 Expanded Polystyrene Foam (Styrofoam) 1-1/2" x 4' x 8' ≈4 lbs
This material absorbs water & has no structural value
Alternate Foam
R-4 Extruded Polystyrene Insulation (25 PSI Compressive Strength) 3/4" x 4' x 8' ≈3 lbs
For above grade or below grade applications – does not absorbs water
This is a structural rigid foam and hard to damage (dent). It would only require a “skin” on the outside, for weather protection.