Disclaimer: if you love your nativity scene and don’t want anybody messing with it, you might want to stop reading here. Just FYI. Otherwise, keep goin’. Fun times are ahead.
First of all, the wise men were not at the birth scene. According to Matthew, they didn’t arrive until Joseph, Mary, and Jesus were living in a house and Jesus was probably 2 years old. Already, your nativity scene is getting less crowded.
Also, there was no mean inn-keeper (sorry to burst your bubble, all of you whose dramatic career consisted of playing this one character in the church Christmas pageant). There was probably no inn, either. According to what I’ve learned, the Greek word used for inn in Luke 2 is probably better rendered as “guest room” and was most likely in back of the ancestral home where the family beast of burden would normally stay.
That means there weren’t animals at the birth scene. Again, not 100% for certain, but more than likely not. I don’t know if any little boy showed up and serenaded the Christ child with a drum solo, but it’s doubtful.
As far as the wise men are concerned, there’s no indication in Scripture that there were three of them. Just because there were three gifts doesn’t mean that there were three of them. And they may or may not have been named Gaspar, Melchior, and Balthasar. For all we know, they could have been named Larry, Curly, and Moe.
The one thing that’s right about your nativity scene is that Jesus is there. The Word became flesh and pitched his tent among us. God took on human skin and became Immanuel– “God with us.” The Almighty became an embryo and the Creator became a helpless infant boy.
So you can keep that part of your nativity scene. You can even add in snow if the spirit leads. But remember that Jesus was probably born in spring, not December, so there was likely no snow that night. I just burst yet another bubble of yours. You’re welcome.

No snow… Make it look like spring or summer, which was more likely when Jesus was born.
I stand corrected. You are right. Take that snow out of the nativity scene again.