Download & install OpenIV
Once installed, open OpenIV & hit 'Ctrl+F3' & search for 'skydome.ytd' (Hint: 'Search in "mods" folder only'). It should be here:
Open the 'skydome.ytd' in openiv by double-clicking it & you will be presented with OpenIV's Texture Editor & a screen like this:
Export the 'moon-new' texture with the '[ Export selected ]' button (bottom left).
It will be exported as a '.dds' texture as default but you can also change the 'Save as type' dropdown to export the file as '.png', '.jpg' or '.bmp' if this is easier to work with (ideally, if you can't use '.dds' you want to use '.png' as then you will still have the use of transparency ).
You then use something that can open & edit '.dds'/'.png' textures like Photoshop with either of these plugins installed:
Generally, you only need to install one of the plugins but if you run into problems exporting try the other one.
More on dds export settings in this post here
Replace the file in the game using OpenIV's 'Texture Editor' by hitting the '[Replace]' button (top right) & locating & opening the edited texture.
Then hit '[Save]' (bottom right) to save the '.ytd'.
That's the basics of the process anyway. Should get you started