Assuming a 360 day year, are the following temperatures for five years random?
Let's crank the number of years up to 100, and overlay the years on top of one another.
Whoops? Kinda got some stair-steps going on there. The weather simulation algorithm is from the "Advanced Dungeons and Dragons Wilderness Survival Guide" (Kim Mohan, 1986) though I did throw in a bit of randomization on the temperature for each day, the above being the daily lows for Temperate zone Mountains. A more accurate simulation can probably be had by playing around with sin waves (maybe slow plus fast plus noise?) but weather simulation is a very deep rabbit hole that I'm mostly refusing to explore more.
Granted, the stereotypical fur-clad barbarian from the north generally cannot tell the exact temperature (lacking a thermometer, or not caring to use it even if the technology is available); colder, colder, about the same, warmer, much warmer would probably suffice for gameplay. If relevant, mostly only survival type games are keenly interested in the weather, while those more towards the storyside will instead have a plot point of the stereotypical wizard messing around with the mountain weather, if the weather is mentioned much or at all ("building character by suffering weather" is also acceptable). That is to say, a barbarian may not notice the stair-step, even if they live long enough, which is unlikely. At best they might have an intuitive sense of "it gets warmer quickly around this time of the year" and thus a festival or something?
You could have a story where the plot point is that the weather really does stair-step, though deriving that fact might be less exciting than watching paint dry, unless collating and doing statistics on numbers is your thing. For the story, you might imagine that there are weather control satellites, so there really is a stair-step observed as the satellites work through some rather stupid code for what temperature to maintain at what time of year.
P.S. How the weather satellites stay in orbit and keep working long enough so that everyone forgets that they are up there and doing things is left as an exercise for the reader. For those who demand answers—look, squirrel!
