Supertux definitely does have that effect (I hate it ;). I only played the original Mario in emulators, so I can't tell you whether it's copied from original.
SMB3 has some sliding, more if you are on ice surface. Supertux has a wee bit less than SMB3 on ice surface, but all the time. I guess that´s intended as, well, you are a penguin on an icy world! :)