Yes, it can be done, but to do it well is a lot of work. You will also need to use a thinner gauge than 1/32" to get the weight down.
Note that one of the very first all-metal aircraft was made of 0.2 mm (1/128") sheet steel and flew well. However, building it required a corrugated substructure and a welded steel tube frame for strength. Still, it was heavier than necessary so its builder switched to aluminium for later designs.
Generally, the tension length of steel (strength relative to density) is roughly equal with that of aluminium or titanium; however, you will need to use high-grade steel to be comparable with aircraft-grade aluminium, so some of the price advantage will be lost.
But there is a distinct disadvantage with higher-density materials. While their strength scales linearly with wall thickness, their buckling strength scales with the square of their thickness. You will end up with a very delicate structure which will require careful handling to avoid local dimples and a stiff substructure to avoid early failure in compression. Also, introducing loads locally (say, for a landing gear or an engine mount) will require local reinforcements which should ideally be multi-layered and taper out in several steps.
If you want to scale an existing structure down, make sure you place the stiffeners closer than what a scale construction would require. But I am sure you will prefer to bond the sheet steel to a styrofoam core. Use a higher-density styrofoam with better compression strength and be generous with local reinforcements, and the model should turn out fine.