You know, I am not sure what the cost is - though I am certain someone will pop in with the prices for you - but they definitely DO have caricature artists around DLR. I can tell you two locations I know of off the top of my head, but I bet there are more than just these. One location is in New Orleans Square, kind of near the Blue Bayou, I think (unless they moved). That is the last place I saw them. There is also usually a caricature artist set up on the Disneyland Hotel grounds. When we have been walking around the DLH property en route to Goofy's Kitchen or something, we have seen the little kiosk/wagon set-up for the artist. So those are 2 definite places to find them. I THINK - though am not 100% positive - that I have also seen a caricature artist in DTD. Could be wrong on that. I am sure there are more inside of DL and in DCA.
Yeah well Ive seen them set up right where you can see the Autopia Tracks right infront of the matterhorn bob sleds loading dock (Close to IASW). I have also seen them in DTD just before you get to the Rain Forest Cafe. There is a big Disney pin cart, and the artist sits close to there (At least this is where I saw him). I thought they were around $20-25
There is the silhouette shop that does silhouettes on Main Street on the east side across from Gibson Girl.
At the exit of Pirates and the Blue Bayou is a long time booth that does sketches of guests.
All others are carts which means it is at the whim of the people in charge of the carts. Only the one in New Orleans Square is permanent and yes I do have mine from back in the 1960"S.