Translation:Yesterday we spent a lovely day in the snow.
yesterday we spent a wonderful day in the snow.
it's not an incorrect translation.
On the snow is also correct, but "in the snow" isn't wrong. In the Northeast it's common to say "we played in the snow". I've never heard anyone here say "on the snow".
Why it is not correct to say 'Yesterday we spent a NICE day in the snow' ???
In an earlier lesson un día hermoso was a nice day. Now it's a lovely day. A nice day and a lovely day is pretty close to the same thing in the US of A and in most parts of Georgia.
When I played IN the snow as a child, I spent a day IN the snow. I've never heard anyone say ON the snow that I can remember.
Whether or not I skied has nothing to do with the fact that the sentence sounds natural to English speakers.
And no, I never skied in my backyard while playing in the snow.