There is no answer to that in Russian or foreign chronicles.
We have no national legends or epics that tried to explain this episode.
Climate around Novgorod is not considerably colder from what we have in Suzdal or Vladimir. The Little Ice Age did not settle in before later.
No archeological evidence has been found so far of Mongol invasion to Russia in the middle of 1200 century.
There are many accounts in Russian and foreign chronicles about devastations to cities i Eastern and Central Europe around the time of the Mongol invasion from a big invasive force from the East. But they don’t give a clear account of its military objective. Much simply does not make sense, like cavalry-based military campaign through Russian woods in the middle of the winter.