You are not supposed to have smoke alarms in the bathroom or just outside of a shower bathroom for this reason actually. Also not in the kitchen. A heat detector is recommended for the kitchen.
I had alarms that would go off specifically in the winter in our stair tower because it was a 200 year old house that was renovated badly with no insulation.
Even my Fibaro smart CO alarm got bugged and drained its entire battery in 2 days because it was in a 5-10C environment (within their specs, but they simply lie on the specs).
From my experience, any life saving device simply can’t handle moderately cold temperatures at all, which is honestly extremely ridiculous to me and very dangerous.
Your problem, if dust related would likely be because you are using optical alarms which are easily susceptible to dust. If that is the case, you could try replacing those with ionization alarms on the 2nd floor. Ionization detects flaming fires better and optical detects very smokey fires better.