What is this WWII four-engine plane on skis?
Looks like a TB-3 or a variant thereof. According to Wikipedia, this four-engine all steel(!) heavy bomber first flew in 1930 and was the world's first cantilever aircraft in this class. The skis do not appear to have pertained exclusively to any specific variant, given that the first flight already used them.

It was used up to and including the Second World War, and a number of experimental variants were developed from it. One of the most interesting was the Zveno project, an experiment with parasite fighters. Here you can see the Zveno-SPB variant of the TB-3 with two I-16 fighters under the wings:



The Zveno-SPB saw operational usage and even success in raids against the Romanian oilfields during WW2.