Maybe it changes how you apply color or if the paper is dark, how it effects what you use to draw in your outline. For me, I realized I really liked starting a painting on this dark ground (this paper had a dark color to it). So I'm going to start my full paintings with a much darker ground then I have in the past.
This Christmas I was at the end of a wrapping paper roll and the core was a length of rolled up craft paper. It struck me that I could probably paint on this stuff! So I rolled it out and laid something heavy and flat on it for a few days so I can get the paper somewhat flattened.
The biggest reason I like oil painting on paper is it's incredibly cheap and thin you can literally do hundred's of sketch paintings on paper and it doesn't take up much room. I use these little painting experiments as loose sketch's and don't take them to seriously. It's good practice though.
So I set up a quick still life of a glass jar and a mushroom. Something this simple is perfect for me, since as a hobbyist I don't have time to do a lot of large finished paintings. I would rather do small quick paintings for fun. Working in this way if I hit on a subject that I like, it might spark an idea for a larger finished painting.
I'll post the process photos below. I started with rubbing a little linseed oil of the surface to let the paint flow better and then using a brush with Burnt Umber I painted in the outlined shapes. Once the proportions are correct it's just a matter of values and colors. Take a look.
I'm blocking in the outline and the shadow areas here. Then it's time for background and foreground. These colors wont all make it to the final but its a good start. It's basically just the local color.
A little further now, Cad-Red for the lid and tweaking the shadow.
Mushroom is added and foreground colors are modified slightly. That about does it for a sketch painting. This took about an hour and half to do and I generally try to keep them to about that long. Let me know if you have any other "found" painting surfaces that you like.