It depends on what you want to achieve.
If you want to improve the look of the character when scaled down, you will most likely want to adjust mipmap generation at your atlas textures.
The simple way to adjust this is to change the texture importer parameter mipmap settings. Please also note that you can adjust the mipmap bias value (this can be set via scrip) if your images get too blurry.
A more advanced way would be to override mipmaps at certain layers manually (with images created in Photoshop), as can be seen in this thread:
UnityでSpineで出力したアトラスにmipmapを手動で追加する方法はありますか？
Apart from that, you could change the skeleton's skin to swap out all attachments at once with lower-resolution versions.
If you do not want to change the look at smaller size but lower the performance impact, it would most likely be the easiest way to create a separate low-res skeleton.
