Is the traditional character for 雪 the same as itself?
These are 2 different fonts for the same character. There are many website to check that, see this post for an overview.

For example on chineseetymology.org and chinese-characters.org you can see that the simplified and traditional characters are identical (the former website explicitely writes: no simplification).

Having said this. Although they are considered to be the same character, people in different regions/countries have habits and the most common way to write something might be different and people might consider some variants as being wrong. This can be seen in the picture below (source zdic.net):