We can't go back in time in every sense of the phrase, but we can go back in time in some sense. And one such sense is that we can go back and see what the weather was like at the time and place. It's called reanalysis, which combines model data with observations from across the world into a globally complete and consistent dataset using the laws of physics. Reanalysis produces data that goes several decades back in time, providing an accurate description of the climate of the past.
Reanalysis is not some kind of magic, but is used quite heavily by scientists. It should not be confused with measurements, which are made at a specific point; reanalysis always shows only averaged values over some area. How accurate is it? Depends on the time, place and particular variable. Using reanalysis in my professional work has yielded very satisfactory results, but with Dyatlov incident, we are talking about a mountainous region in a desolate district in Soviet union - I don't know how much trustworthy meteorological data from this region is used for reanalysis. For checking the validity of data, I should find the measurements from the closest synoptic station, and then compare. I might succeed in doing this.
Anyway, my first attempts with the data can be accessed here:https://heidotrofimov.github.io/
I did not detect anything unusual in this data by myself :) . Actually, in the sense of the weather, 1-2 February 1959 seems remarkably average.