As commented by @CD0139, this is a correct behaviour with Live Weather. Even if you change the date to summer but let the Live Weather on, if Meteoblue is reporting snow to the location you are flying, you’ll see snow into the sim.
If you would like to fly with Live weather condition at another past date, this functionality does not exist into the sim, but there is a wish:
Moved to User Support Hub Weather & Live Weather since this is not a bug.