Arthur does have a crying scene after breaking a present for his mother which is shown as an emotional breaking point. This may or may not be upsetting depending on the viewer. Buster's mother in most of her scenes is shown extremely anxious and lacking sleep, freaking out about Christmas and trying to make Buster happy.
Though there is a scene where DW thinks Santa is in the bathroom and she runs in while Arthur is using the restroom. Nothing is shown but it is played for laughs.
Subtle implications from Arthur's mother that Santa "can't always get people exactly what they want" to DW when she gets upset about not getting a Cat themed toy/doll she wanted. There is no straight out denials of Santa's existence nor is he ever really shown in the movie.
Another scene shows their Uncle shaving in the mirror while in his red pajamas, DW sees him and thinks he's Santa so runs to grab her dad.